Self-assembled and ordered growth of silicon and germanium nanowires

Self-assembled and ordered growth of silicon and germanium nanowires

Superlattices and Microstructures 46 (2009) 277–285 Contents lists available at ScienceDirect Superlattices and Microstructures journal homepage: ww...

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Superlattices and Microstructures 46 (2009) 277–285

Contents lists available at ScienceDirect

Superlattices and Microstructures journal homepage:

Self-assembled and ordered growth of silicon and germanium nanowires Andrea Kramer ∗ , Martin Albrecht, Torsten Boeck, Thilo Remmele, Peter Schramm, Roberto Fornari Leibniz Institute for Crystal Growth, Berlin, Germany



Article history: Available online 9 December 2008 Keywords: Nanowires Silicon Germanium Orientation Physical vapor deposition Substrate structuring Focused ion beams

abstract Self-assembled and ordered silicon and germanium nanowires grown by physical vapor deposition (PVD) via vapor–liquid–solid (VLS) mechanism are presented. The morphology of the nanowires has been investigated by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Differences in the orientation of the homoepitaxially grown nanowires between silicon and germanium were observed. Most silicon nanowires grew in [111] direction on the (111) Si substrate whereas germanium nanowires grew in h110i direction on the (111) Ge substrate. Nucleation energies as a function of supersaturation were considered. The results of these calculations could explain the behavior of Si and Ge wires in terms of growth direction. A method to position nanodroplets and thus to obtain a regular arrangement of nanowires is also presented. For this purpose, substrates were structured with nanopores by focused ion beams (FIB) before inserting them into the growth chamber. Gold droplets have been successfully ordered both on silicon and on germanium substrates. A regular array of epitaxial silicon nanowires has been obtained as well. © 2008 Elsevier Ltd. All rights reserved.

1. Introduction Silicon and germanium nanowires are of great interest in the field of nanoelectronics as they represent promising building blocks for the bottom-up approach of nanodevices. Field effect transistors with good device properties have been fabricated from single silicon and germanium

Corresponding author. Tel.: +49 30 6392 3050. E-mail address: [email protected] (A. Kramer).

0749-6036/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.spmi.2008.10.041


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nanowires [1,2] as well as from Si/Ge nanowire heterostructures [3]. For the integration of silicon and germanium nanowires in electronic devices it is however essential to control their size and position reproducibly. Furthermore, most devices are on (001) substrates, thus it is necessary to favor nanowire growth in certain crystal directions, preferably the [001] direction [4]. Among several methods to grow silicon and germanium nanowires, chemical vapor deposition (CVD) is the most widely applied. On the other hand, physical vapor deposition (PVD) is appropriate for studying the basic mechanisms and the beginning of growth, as the atoms arrive singularly at the substrate surface with lower rates compared with CVD. In this paper, the growth of silicon and germanium nanowires by the well-known VLS mechnism via PVD will be shown and discussed, especially with regard to orientation and position of the wires. The different orientations of silicon and germanium wires will be explained based on the calculation of nucleation energies on different crystal facets. It will be further shown that the position of the wires can be influenced by pre-structuring substrates by FIB. 2. Experimental The cleaning procedure for silicon substrates consisted of an RCA standard process and an HF-dip, as already reported elsewhere [5]. Germanium substrates were cleaned for at least 120 s in ammonia aqueous (28% NH4 OH:deionized water = 1:4) following the procedure suggested by Akane et al. [6] to achieve a complete etching of the native oxide. All experiments were performed in an ultra-high vacuum (UHV) chamber with a background vacuum of about 2.5 × 10−9 mbar. The first step of the procedure was the desorption of residual oxide which could form during loading the substrate into the chamber. This was performed at a substrate temperature of 850 ◦ C for silicon and at a substrate temperature of 750 ◦ C for germanium. The second step was the evaporation of gold from an effusion cell at a substrate temperature of 550 ◦ C for silicon and 450 ◦ C for germanium. Afterwards, either silicon by electron beam evaporation or germanium from an effusion cell was deposited at a rate of about 0.5 Å/s. For SEM imaging of the sample surface and for substrate pre-structuring, an FEI NanoLab dual beam system was used. This equipment allows simultaneous analysis of the structure by SEM and structuring of the surface by focused 30 kV Ga+ ions. The distances, widths and depths of the nanopores can be controlled by the ion beam settings blank time, current, and dwell time, respectively. TEM measurements were performed using a JEOL JEM 2200FS. 3. Results and discussion 3.1. Growth of silicon nanowires on Si(111) Silicon nanowires grew epitaxially in [111] direction on (111) Si wafers which was verified by TEM measurements (Fig. 1). The results show unambiguous correlations between the obtained wires and the experimental parameters growth temperature and growth time (Fig. 2) and were reproduced well. A higher substrate temperature leads to higher gold diffusion and thus to thicker droplets and wires. A longer evaporation time leads to longer whiskers with the same distribution. The grown layer inbetween the wires shows triangular structures resulting from the (111) orientation of the substrate. The results are consistent with reports in the literature [7,8]. 3.2. Growth of germanium nanowires on Ge(111) The growth of Ge nanowires differed considerably from the growth of Si nanowires. Short and thick structures grew in the [111] orientation of the substrate, but long nanowires followed a h110i direction as is shown in Fig. 3 on the right. On the left side of Fig. 3, results of silicon nanowire growth are again shown for comparison. By TEM investigations, it was shown that the germanium wires initially grew epitaxially in [111] direction on the substrate which can be seen on the HRTEM image (inset of Fig. 4). The wires then changed their orientation into a h110i direction (Fig. 4).

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Fig. 1. TEM image of a silicon nanowire grown epitaxially on silicon (111).

Fig. 2. SEM images of silicon nanowires on silicon (111) grown at different growth temperatures and evaporation times.

3.3. Thermodynamic consideration of silicon and germanium nanowire growth In the literature there are several reports about nanowires growing in h110i direction and related thermodynamics. Wu et al. [9] found silicon nanowires predominantly growing in h110i direction if they had a diameter between 3 and 10 nm. For those wires they found that the solid/vacuum interfaces were the lowest-free-energy (111) and (100) planes. They explained that fact by the important role of surface energies for such thin nanowires. This could also be an explanation for our small wires on silicon (Fig. 8) but it cannot account for our rather thick germanium wires. Germanium nanowires both along the h111i and the h110i direction have been observed by Adhikari et al. [10]. They assumed that screw dislocations could be an explanation although they found no evidence of screw dislocations in their Ge nanowires. Kim et al. [11] investigated the growth of germanium nanowires on silicon and on GaAs. On silicon, in contrast to our results, they did not get any epitaxially grown wires whereas on GaAs, they got growth in h110i direction. They assume to have a certain amount of As/Ga dissolved in Au at the initial state of growth and thus incorporation of these species into the nanowire which could result in


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Fig. 3. Top: Tilted SEM images of a Si and a Ge wire and a sketch of facets of the Si and Ge crystal. Bottom: SEM images of Si and Ge wires and sketch of the projection of the [111] and the h110i directions onto a (111) surface.

Fig. 4. TEM images of germanium nanowires grown on germanium (111). The inset shows a HRTEM image of the interface substrate-wire.

change of the lattice parameter. According to the hypothesis of Kim et al., the nanowire then chooses a growth direction to minimize the strain. Ge et al. [12] found that supersaturation could be a reason for the growth of silicon nanowires on silicon (111) once vertically and under certain conditions along the other h111i directions. An interesting approach regarding the influence of strain and of supersaturation on nanowire growth by molecular beam epitaxy can be found in [8]. Zakharov et al. found out that supersaturation is determined by the interplay between elastic stresses and surface energy. They calculated the difference between chemical potentials of silicon atoms in the overgrown layer and on the top of the wire. On this basis, they explained the growth kinetics and the relationship between radius and length of wires. However, they did not consider the orientation of the wires.

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Fig. 5. 2D nuclei on different surfaces of the Si or Ge crystal.

To explain the different orientations between silicon and germanium nanowire growth, nucleation energies on different crystal facets were considered. We followed the idea of Grzegory et al. [13] who calculated a change in Gibbs free energy related to the formation of 2-dimensional (2D) nuclei on different surfaces of GaN. The surface orientation determines the form of the nucleus as well as the number of the resulting additional broken bonds which are created. On the basis of the lattice geometry the 2D nuclei on the three main surfaces can be derived (Fig. 5). The assumption of 2D nucleation i.e. layer by layer growth, is reasonable because it has been seen by TEM for heterostructures in semiconductor nanowires that the junctions are atomically sharp [14]. In Fig. 5 the large dots correspond to the uppermost level of the nucleus while atoms located underneath are drawn smaller. The size of the nuclei is parameterized by m, which is the number of atoms along one side of the nucleus. The total number of atoms n as well as the number of additional unsaturated bonds q are functions of m. The variation of free energy 1G, does depend on changes of volume and surface of the nucleus while it expands and reaches a stable dimension. The volume term is negative and proportional to the number of atoms in the nucleus: −n(m)1µ · 1µ is the difference in chemical potential of the single atom before and after being incorporated into the nucleus and can be expressed as function of temperature and supersaturation S:

1µ = kT · ln S .


The surface term is positive and proportional to the number of additional dangling bonds which result from extending the surface of the nucleus: q(m)Φ · Φ is the energy of a dangling bond. Thus, for 1G the following holds:

1G(m) = −n(m) · 1µ + q(m) · Φ .


To determine m , the number of atoms along one side of the critical nucleus, the derivative of 1G with respect to m has to be equal to zero. Inserting m∗ into Eq. (2) results in 1G∗ , the energy necessary to form a critical nucleus. As 1µ, also 1G∗ is a function of temperature and supersaturation. For the three different surfaces, the following relations are found: ∗


1G∗ (111) = − kT · ln S + 2

Φ2 3 kT · ln S 8


Φ2 2 kT · ln S 1 Φ2 1G∗ (100) = . 2 kT · ln S 1G∗ (110) =


Φ is not known for the growth from solution. From a qualitative plot which compares the nucleation energies of the (111) and the (110) surfaces (Fig. 6), it can be seen that at lower supersaturation, nucleation on (110) is favored whereas at higher supersaturation, nucleation on (111) is favored. The intersection is for higher temperatures at lower supersaturation. This is valid for both silicon and germanium. Because the energy of a Si–Si bond (3.73 eV) is larger than the one of a Ge–Ge bond (3.56 eV) [15], also Φ is supposed to be larger for silicon than for germanium.


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Fig. 6. Critical nucleation energy against supersaturation at two temperatures on (111) and (110) surfaces of the Si and Ge crystal.

Fig. 7. SEM images showing the influence of higher rates and temperatures on Ge nanowire growth.

Fig. 8. Silicon nanowires on Si(111) grown in h110i direction.

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Fig. 9. FIB pre-structuring of substrates. Left: Structure on germanium. Middle: Structure after gold evaporation. Right: Structure with one nanodroplet per nanopore after adjustment of the experimental parameters.

Fig. 10. Growth of Si nanowires on a pre-structured substrate.

If our assumptions are correct, it is possible that the first nucleus, which is in the case of a (111) substrate always (111) orientated, exhibits facets with other orientations. If then nucleation is favored on another facet than (111), growth can also proceed in other directions. From the diagram (Fig. 6) one can conclude that growth is favored on (111) surfaces at high temperature and high supersaturation. Experimental results at different rates and temperatures confirmed the validity of our assumptions (Fig. 7): at a higher substrate temperature – 550 ◦ C compared with 430 ◦ C – or a higher supersaturation – a rate of about 1.5 Å/s compared with a rate of about 0.5 Å/s – germanium growth proceeded preferably in [111] direction.


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Fig. 11. Growth of Ge nanowires on a pre-structured substrate.

From the obtained results on germanium we concluded that growth in another direction should also be possible on silicon when proper growth conditions are chosen. The first experiments have been performed: we applied a very low silicon rate < 0.1 Å/s. The results shown in Fig. 8 clearly indicate that also silicon nanowires may grow along h110i direction, in agreement with our model. To find a detailed description for the growth of nanowires in different directions, there are still more investigations necessary. 3.4. Ordered growth of silicon and germanium nanowires For the arrangement of nanowires, substrates have been pre-structured by focused ion beams. After adjustment of gold rate and substrate temperature during evaporation, perfect arrays of ordered gold droplets on silicon as well as on germanium substrates were obtained (Fig. 9). Silicon nanowires from an array of gold droplets could be successfully grown (Fig. 10). However, for some unknown reason, it was not possible to grow a wire from every droplet. Growth seems to be strongly dependent on the surface state. But in principle it is possible to heal the lattice damaged by FIB during growth and to array silicon nanowires. In the case of germanium, it was seen to be much more difficult to order the wires (Fig. 11). Our explanation for this fact is again based on the tendency for germanium wires to growth in different direction in comparison with silicon wires. 4. Conclusion Silicon and germanium nanowires grown by PVD via VLS mechanism have been investigated especially with regard to their orientation and position. Germanium nanowires showed a completely

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different behavior as their growth orientation was h110i at our experimental conditions. To explain this difference in comparison with silicon, nucleation energies on different surfaces have been considered and calculated as a function of supersaturation. A qualitative agreement between orientation of the wires and supersaturation range was found. At a higher temperature and a higher supersaturation in the solution droplets, growth occurred also on germanium predominantly in [111] direction. Nanodroplets have been positioned by pre-structuring substrates by FIB. Gold droplets have been successfully ordered both on silicon and on germanium substrates. A regular array of epitaxial silicon nanowires has been obtained while for germanium no one-to-one correlation with the positioned droplets was found. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]

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