Growth characteristics of silicon nanowires synthesized by vapor–liquid–solid growth in nanoporous alumina templates

Growth characteristics of silicon nanowires synthesized by vapor–liquid–solid growth in nanoporous alumina templates

Journal of Crystal Growth 254 (2003) 14–22 Growth characteristics of silicon nanowires synthesized by vapor–liquid–solid growth in nanoporous alumina...

551KB Sizes 3 Downloads 52 Views

Journal of Crystal Growth 254 (2003) 14–22

Growth characteristics of silicon nanowires synthesized by vapor–liquid–solid growth in nanoporous alumina templates Kok-Keong Lew, Joan M. Redwing* Department of Materials Science and Engineering, Materials Research Institute, The Pennsylvania State University, University Park, PA 16802, USA Accepted 14 March 2003 Communicated by K.H. Ploog

Abstract The fabrication of Si nanowires has been demonstrated using a combination of template-directed synthesis and vapor–liquid–solid (VLS) growth. The use of nanoporous alumina membranes for VLS growth provides control over nanowire diameter while also enabling the production of single crystal material. An investigation of the growth characteristics of Si nanowires over a temperature range from 400 C to 600 C, and over a SiH4 partial pressure range from 0.13 to 0.65 Torr was carried out. The length of Si nanowires was found to be linearly dependent on growth time over this range of conditions. The nanowire growth rate increased from 0.068 mm/min at 400 C to 0.52 mm/min at 500 C at a constant SiH4 partial pressure of 0.65 Torr. At temperatures greater than 500 C, Si deposited on the top surface and pore walls of the membrane thereby reducing the nanowire growth rate. The growth rate versus temperature data was used to calculate an activation energy of 22 kcal/mol for the nanowire growth process. This activation energy is believed to be associated with the decomposition of SiH4 on the Au–Si liquid surface, which is considered to be the rate-determining step in the VLS growth process. r 2003 Elsevier Science B.V. All rights reserved. PACS: 81.05.Ys; 81.05.Cy; 81.15.Gh Keywords: A1. Growth models; A2. Growth from vapor; A2. Vapor–liquid–solid; B1. Nanomaterials; B2. Semiconducting silicon

1. Introduction In the last few years, nanomaterials, which are of fundamental and technological interest, have attracted increasing attention since carbon nanotubes were first discovered in the 1990s [1]. The main driving force is the shrinking feature size of *Corresponding author. E-mail address: [email protected] (J.M. Redwing).

silicon (Si) CMOS devices, in which the critical dimension is anticipated to be below 0.1 mm by 2007. This small length scale presents immense technical challenges for manufacturing processes, such as photolithography and interconnects. As a result, there is increasing interest in the synthesis and assembly of nanomaterials, such as nanotubes and nanowires, which may serve as the building blocks for the next generation of electronic devices.

0022-0248/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-0248(03)01146-1

K.-K. Lew, J.M. Redwing / Journal of Crystal Growth 254 (2003) 14–22

Semiconducting nanowires have recently attracted increasing interest due to the unique fundamental properties and potential applications of these structures. Boron-doped Si nanowires, for example, have been used for sensor applications such as pH and protein binding [2]. Recently, Gudiksen et al. [3] demonstrated the fabrication of gallium arsenide (GaAs)/gallium phosphide (GaP) nanowire superlattices and Si nanowire p–n junctions which may find applications in nanoscale electronics and photonics. A common process for semiconductor nanowire synthesis is vapor–liquid–solid (VLS) growth. The well-known VLS mechanism for Si nanowire growth was initially proposed and demonstrated by Wagner and Ellis [4,5]. In this process, gold (Au) is used to catalyze the decomposition of a Sicontaining source gas, such as silane (SiH4) or silicon tetrachloride (SiCl4). Au and Si then form a liquid phase alloy at a eutectic temperature of 363 C. Finally, Si nanowires crystallize and grow from the supersaturated alloy. In this process, the diameter of the nanowire is determined by the original size of the Au catalyst particle as well as growth conditions. Synthesis of Si nanowires with different diameters has been demonstrated using techniques in which the Au particles were formed by metal deposition and photolithography (o20 mm) [6,7], laser ablation (6–20 nm) [8], evaporation (B15 nm) [9] or nanocluster formation (6–31 nm) [10]. The majority of studies of VLS growth carried out thus far have focused on the effect of metal catalyst size and growth conditions on the structural properties of the nanowires. The effect of processing parameters on the growth rate of the nanowires has not been examined in detail. The impact of growth temperature and SiH4 partial pressure on the structural properties of Si nanowires was reported by Westwater et al. [11,12] The optimum conditions for growing straight, single crystal Si nanowires on the surface of a Si wafer were at moderate temperature (B600 C) and at low total pressure (B0.1 Torr). In this study, nanoporous membranes were used as templates to control the diameter of VLS-grown Si nanowires. This technique combines the advantages of both template-directed synthesis and

15

VLS growth to produce straight, single crystal Si nanowires with well-controlled diameters ranging from 100 to 340 nm [13]. Si nanowires grown out of the membranes were found to be either single crystal with growth orientation /1 0 0S [13] or bicrystalline containing a single (1 1 1) twin boundary along the ½1 1 2%  growth axis [14]. Template-directed synthesis provides a convenient platform to study the effect of process parameters on nanowire growth since the nanowire diameter is determined by the pore size of the membrane rather than the growth conditions. In this study, the effect of growth temperature and SiH4 partial pressure on the growth rate of the nanowires was investigated. The experimental results are compared with those previously reported for lowpressure chemical vapor deposition of Si from a SiH4 source.

2. Experimental procedure Commercially available anodic alumina membranes (Whatman Scientific) with a nominal pore diameter of 200 nm and thickness of 60 mm were used as templates in this study. Alumina membranes with pore diameters ranging from 4 nm to greater than 200 nm can be produced through the anodization of aluminum in various acids as described by Routkevitch et al. [15]. A schematic of the nanowire fabrication process is as shown in Fig. 1. The Au catalyst for VLS growth was electrodeposited into the membranes using a process described by Martin et al. [16]. A thin layer of Ag was initially deposited on the backside of the membrane by sputtering or thermal evaporation (Fig. 1(b)). In order to control the placement of the Au catalyst relative to the top surface of the pore, a 10–30 mm long segment of silver (Ag) was deposited in the pores, followed by a thin (0.2–0.75 mm) segment of Au (Fig. 1(c)). The Ag was then removed by etching in 8.0 M HNO3, leaving only the thin Au segment near the center of the membrane (Fig. 1(d)). The membrane was cleaned with distilled water in an ultrasonic bath and dried under ambient conditions. VLS growth experiments were then carried out in an isothermal 100 diameter cylindrical quartz

16

K.-K. Lew, J.M. Redwing / Journal of Crystal Growth 254 (2003) 14–22

Fig. 1. Schematic of the nanowire fabrication process. (a) Blank nanoporous alumina membrane. (b) A thin layer of Ag was first either sputtered or thermally evaporated on the back of the membranes. (c) Segments of Ag followed by Au plugs were electrodeposited into the pores. (d) HNO3 of 8.0 M was used to etch away the Ag leaving the Au plugs in the membrane. (e) VLS growth was performed using SiH4 to grow Si nanowires within the pores. (f) Si nanowires were released by etching away the membrane after growth.

tube reactor. The Au impregnated membrane was placed in a quartz boat, which was situated in the middle of a 2000 long-quartz tube inside a tube furnace. The system was degassed under vacuum and purged with N2. The process gas was then switched to H2 and the membrane was heated to the growth temperature (400–600 C). A 5% mixture of SiH4 was then introduced into the reactor to initiate nanowire growth (Fig. 1(e)). The total flow rate in the reactor was 100 sccm and the total pressure in the reactor was held constant at 13 Torr. Experiments were performed to investigate the effects of temperature (400–600 C) and SiH4 partial pressure (0.13–0.65 Torr) on the growth rate of the nanowires. The nanowires can be released by etching away the membrane in 0.5 M NaOH (Fig. 1(f)), however, for the growth experiments described in this study, the nanowires were left in the membrane for characterization.

Plan view and cross-sectional images of the membranes after VLS growth were analyzed using a 30 kV Philips XL20 scanning electron microscope (SEM). The membrane top and bottom surfaces after growth were analyzed to ensure that the Si nanowires did not grow out of the pores. The length of the nanowires was measured by analyzing different areas of the cross-section of the membrane using SEM after VLS growth.

3. Model of SiH4 diffusion and reaction in a nanopore VLS growth in nanoporous templates requires careful consideration and selection of reaction conditions. In conventional VLS growth, the metal catalyst particle is either supported on a surface or produced in the gas phase and is readily accessible

K.-K. Lew, J.M. Redwing / Journal of Crystal Growth 254 (2003) 14–22

to the vapor phase growth species. In templatedirected VLS growth, the metal catalyst particle is buried deep within the pore. Consequently, a careful choice of reaction conditions is required to ensure that the vapor phase species diffuses far into the pore and preferentially reacts with the metal catalyst rather than the internal walls of the pore. These conditions can generally be met at reduced temperatures and pressures, although the specific range of conditions will depend on the homogeneous and heterogeneous reaction kinetics of the vapor phase source used for nanowire growth. An initial study of the diffusion and reaction of SiH4 in anodic alumina templates was carried out in order to define a range of conditions for the VLS growth of Si within a nanopore. The extent of reaction of SiH4 along the length of a nanopore was predicted as a function of growth conditions using the mathematical treatment of diffusion and reaction within a cylindrical pore [17]. Assuming steady state and a first-order reaction, the concentration of SiH4, CA ; as a function of position, z; within a pore of radius r and length L can be described by pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi e DaII ð1z=LÞ þ e DaII ð1z=LÞ pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi CA ¼ CA;s ; ð1Þ e DaII þ e DaII where DaII ¼

ks ðAin Þv L2 De

ð2Þ

is called the second Damkohler number and describes the ratio between the rate of chemical reaction at the inner surface of the pore and the rate of material transport into the pore by diffusion. In Eq. (1), CA;s is the concentration of SiH4 at the pore inlet. In Eq. (2), ks is the rate constant of the heterogeneous reaction, ðAin Þv is the internal surface area of the pore per unit volume, and De is the effective diffusion coefficient. Diffusion of molecules at low pressure (o10 Torr) within 2–200 nm diameter pores proceeds in the Knudsen regime. In this case, the effective diffusivity can be described as De ¼ dv=2 where d is the pore diameter and v is the mean speed of the molecules. The surface rate constant

17

for SiH4 decomposition, ks ; was estimated from kinetic theory as the product of the impingement rate and the reaction probability of SiH4 on a Si surface [18]. The predicted concentration of SiH4, CA ; (normalized to its concentration at the pore inlet, CA;s ) along the length of nanopore (z) is plotted in Fig. 2. A schematic diagram of the pore geometry used in the calculations is included as an inset in this figure. The pore diameter used in the calculations was 200 nm and the pore length to the surface was 25 mm, similar to the experimental conditions. As shown in Fig. 2, low growth temperatures (p500 C) are required in order for SiH4 to diffuse far into the pore without substantial wall or surface deposition. Prior studies using SiH4 as the Si source have demonstrated nanowire growth by VLS at temperatures as low as B320 C [12]. Above 500 C, Si is predicted to also deposit on the membrane surface and internal pore walls and potentially block the diffusion of SiH4 to the Au catalyst. Figs. 3(a) and (b) are scanning electron micrographs of the membrane surface after 60 min of growth at 505 C and 540 C at a constant SiH4 partial pressure of 0.65 Torr. Minimal Si deposition was observed on the membrane surface after 60 min of growth at 505 C (Fig. 3(a)) while substantial deposition and near pore closure was observed at 540 C for a comparable growth time (Fig. 3(b)). The results of these initial studies indicate that a temperature range from 363 C to 500 C should be suitable for the VLS growth experiments.

4. Experimental results 4.1. Effect of temperature The effect of temperature on the growth rate of the Si nanowires was initially investigated. Au plugs with an average thickness of 0.24 mm were electrodeposited into the nanoporous membranes at a distance of 25 mm from the membrane surface. Growth experiments were then performed at times ranging from 2 to 40 min, growth temperatures between 400 C and 500 C, a total pressure of 13 Torr and a SiH4 partial pressure of 0.65 Torr.

18

K.-K. Lew, J.M. Redwing / Journal of Crystal Growth 254 (2003) 14–22

T=500o C 1.0

T=800o C

CA /CA,s

0.8

0.6

T=1000o C

Boundary layer

CA,s 0.4 z L

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

z/L Fig. 2. Predicted concentration profiles of SiH4 (CA ) as a function of position z within a 200 nm diameter by 25 mm long pore at different temperatures. Low temperatures are required for SiH4 to diffuse to the base of the pore without substantial surface and wall deposition. (Insert) A schematic diagram of the nanopore geometry used in the model calculations. CA;s is the concentration of SiH4 at the boundary layer, CA is the concentration of SiH4 at a distance z from the top of the pore, and L is the total pore length. The arrows illustrate the diffusion of SiH4 into the pore, reaction on the pore wall, and the diffusion of H2 gas out of the pore.

Fig. 4 shows a cross-section of the membrane after 8 min of growth time at 500 C. Si nanowires grow in both directions from the initial position of the Au catalyst as indicated in the figure. SiH4 can diffuse into the pore from both sides of the membrane under the experimental conditions described above. This is likely responsible for nanowire growth in the two directions that was observed. The Au caps on each end of the nanowire are approximately 0.12–0.14 mm thick, which is roughly half of the original Au plug thickness (0.24 mm). As a result of the formation of the Au–Si eutectic liquid phase, the Au caps are hemispherical in shape due to surface energy minimization. Some of the Au was retained in the original position after the VLS growth creating a distinct band in the membrane cross-section (Fig. 4). The band could also be due to discussion of the Au–Si liquid alloy phase between the pores if there are holes or imperfections in the pore walls. The average length of the nanowires as a function of growth time for temperatures ranging from 400 C to 500 C is shown in Fig. 5. The length of nanowires was determined by measuring the distance between the two Au tips on each end,

subtracting the thickness of the original Au plug, and dividing this number in half. The growth rates reported in this study are therefore corrected for the bi-directional growth in order to compare with the growth rate of nanowires on a surface. The nanowire growth rate was determined from the slope of the lines in Fig. 5. The growth rate of the Si nanowires was found to have a strong dependence on temperature ranging from 0.068 mm/min at 400 C to 0.52 mm/min at 500 C. The growth rate of the Si nanowires as a function of temperature, shown in Fig. 6, was used to calculate an activation energy (Ea ) for the nanowire growth process. In addition to the growth rate data from Fig. 5, which was obtained with a Au thickness of 0.24 mm, data obtained with a Au thickness of 0.75 mm was also included in Fig. 6 for comparison. At low temperatures (o500 C), the growth rate versus temperature data follows an Arrhenius dependence. The activation energy in this region was determined to be 22 kcal/mol from the slope of the line for the 0.24 mm Au thickness experimental data. As shown in Fig. 6, the 0.75 mm Au thickness data exhibits a similar activation energy as that obtained with 0.24 mm of Au. At temperatures greater than

K.-K. Lew, J.M. Redwing / Journal of Crystal Growth 254 (2003) 14–22

500 C, the growth rate begins to decrease with increasing temperature. On these samples Si was observed to deposit on the membrane surface (as

(a)

1 µm (b)

19

shown in Fig. 3(b)) and internal pore walls thereby decreasing the growth rate of the nanowires in this temperature range. The experimental results are in good agreement with the model predictions discussed in Section 3. The activation energy for VLS growth of Si nanowires measured in this study (22 kcal/mol) is considerably smaller than that of conventional low-pressure chemical vapor deposition (LPCVD) of Si growth from a SiH4 source (34.5–40 kcal/ mol) [19]. The smaller activation energy measured in this study is attributed to the catalytic effect of Au in the VLS growth process and also explains the higher growth rate of Si nanowires by VLS compared to that of Si thin film growth [20]. Bootsma et al. [21] reported an activation energy of 11.9 kcal/mol for the VLS growth of Si whiskers on a Si wafer from SiH4 at temperatures between 550 C and 900 C, which is similar to the results obtained in this study. 4.2. Effect of silane partial pressure

1 µm Fig. 3. SEM micrographs of the surface of the nanoporous membrane after 60 min of growth at (a) 505 C and (b) 540 C. The SiH4 partial pressure was 0.65 Torr and the total pressure was 13 Torr in both cases.

Initial location of Au

The effect of SiH4 partial pressure on Si nanowire growth was also investigated. The experiments were conducted at a constant temperature of 500 C and a total pressure of 13 Torr using a 0.24 mm thick Au segment. The growth time was fixed at 20 min while the SiH4 partial pressure was changed from 0.13 to 0.65 Torr by varying the mixture of SiH4 and H2 carrier gas keeping the total flow rate constant at 100 sccm. The nanowire growth rate increased linearly with

Au tips

5 µm Fig. 4. Cross-section of nanoporous membrane after 8 min of growth at 500 C, a total pressure of 13 Torr, and a SiH4 partial pressure of 0.65 Torr. Au tips are observed at both ends of the Si nanowires.

K.-K. Lew, J.M. Redwing / Journal of Crystal Growth 254 (2003) 14–22 0. 0.6

12 T=500 T= 500o C 0.52 µm/ 0.52 m/min min

10

8 T=451o C T=451 0.23 23 µm/ m/min min 0.

6

4

o

T=426 C T=426 0.10 10 µm/ m/min min 0.

2

T=400o C T=400 6.80 x 10-2 µm/ 6.80 m/min min

0 0

10 0

2 20 0

3 30

40

Silicon nanowire growth rate (µm/min) ( m/min)

Length Le ngth of S Silicon licon na nanow nowire re ((µm) m)

20

0.5 0.

0.4 0.

0. 0.3

0.2 0.

0.1 0.

0.0 0. 0.0 0.

0.1

0. 0.2

0.3

0. 0.4

0.5

0. 0.6

0.7

Sila ilane ne pa partia rtiall pressure pre sure ((Torr) orr)

Grow owth th time ((min) in) Fig. 5. Length of Si nanowires as a function of growth time and temperature at a total pressure of 13 Torr and SiH4 partial pressure of 0.65 Torr.

o

Silicon ilicon na nanow nowire ire grow growth th rate rate ((µm/ m/mi min) n)

Temper Tem erat ature e ( C) 1000

1

600

500

400

300

0.1 0.

0.24 µm of Au thickness 0.75 µm of Au thickness 0.6 0.

0.8

1.0 1.

1.2

1.4 1.

1.6

1.8 1.

2.0

1000/T (1/K) (1/K Fig. 6. Arrhenius plot of Si nanowire growth rate at temperatures ranging from 400 C to 600 C at SiH4 partial pressure of 0.65 Torr and 8 min of growth time. Two different Au plug thicknesses (0.24 and 0.75 mm) were used in the experiments.

increasing SiH4 partial pressure as illustrated in Fig. 7.

5. Discussion The VLS growth process can be summarized in the following four steps [22]: (1) mass transport of SiH4 from the gas phase to the Au surface; (2)

Fig. 7. Dependence of SiH4 partial pressure on Si nanowire growth rate at a constant temperature of 500 C and a constant total pressure of 13 Torr. The circles are the experimental data and the line is the linear least-squares fit of the data.

reaction of SiH4 on the Au surface; (3) diffusion of Si through the Au–Si eutectic liquid phase; (4) crystallization of Si from the supersaturated Au–Si eutectic liquid. In this study, the experimental conditions (low temperature, low pressure) were chosen such that the mass transport of SiH4 from the bulk gas phase to the Au surface within the pore (step 1) would not be the rate-limiting step in the process. The diffusion of Si in the Au–Si liquid alloy phase (step 3) is also not believed to be the ratelimiting step because diffusion in liquid metals usually occurs very fast. Since the diffusion coefficient of Si in the Au–Si liquid phase is not available, the self-diffusion coefficient of Si in liquid Si from molecular dynamics calculation [23] was used to estimate the diffusion time of Si over a distance of 0.24 mm. The diffusion time is approximately 1 ms at a growth temperature of 500 C. The fast diffusion time indicates that the diffusion of Si in the Au–Si liquid alloy phase is unlikely to be the rate-limiting step. Furthermore, the activation energy for diffusion in liquid metal is typically in the range from 1 to 4 kcal/mol [24] which is substantially lower than the activation energy measured in the present work (22 kcal/mol). Hence, diffusion of Si in the Au–Si liquid alloy phase is unlikely to be the rate-limiting step. The last step in the growth process (step 4) is the crystallization of Si from the supersaturated Au–Si

K.-K. Lew, J.M. Redwing / Journal of Crystal Growth 254 (2003) 14–22

liquid alloy phase. Due to the lack of information on Si growth from a Au–Si melt, it is difficult to determine if this step is rate limiting in the overall VLS process. If Si crystallization were rate limiting, however, Si would be expected to accumulate on the surface or within the bulk of the Au–Si liquid alloy at high SiH4 partial pressure. This was not observed within the range of conditions used in the experiments. The decomposition of SiH4 on the vapor–liquid surface (step 2) is therefore believed to be the rate-limiting step in the overall process A simple heterogeneous reaction model was developed to predict the nanowire growth rate as a function of growth conditions assuming that step 2 (SiH4 decomposition) is rate limiting. It was further assumed that the homogeneous decomposition of SiH4 was not favored under these low pressure and low temperature conditions (the activation energy required for SiH4 pyrolysis [25] generally falls between 51 and 59 kcal/mol in the temperature ranged from 800 to 1500 K). Therefore, the growth of Si nanowires is likely controlled by the heterogeneous reaction of SiH4 on the Au–Si liquid alloy surface, which can be described by the following overall reaction: k

SiH4ðgasÞ ! Si þ 2H2ðgasÞ ; Au ðsÞ

ð3Þ

where k is the first-order reaction rate constant described by the Arrhenius equation, k ¼ A expð  Ea =RTÞ; where A is the pre-exponential factor and Ea is the activation energy. SiH4 is considered to initially adsorb on active sites on the Au surface and to decompose into Si and H2. H2 then desorbs from the surface and Si diffuses into the Au. As the concentration of Si increases, Au and Si begin to form a liquid phase alloy provided the temperature is above the eutectic temperature (B363 C). The formation of the Au–Si liquid alloy would significantly increase the incorporation of Si into the liquid since the number of available sites on a liquid is not restricted [26]. The rate-limiting step in the process is considered to be the heterogeneous decomposition of SiH4 on the Au–Si liquid alloy surface from previous discussions. As a result, the calculated activation energy from the Arrhenius plot of Fig. 6

21

would correspond to the reaction of SiH4 at the Au–Si liquid surface (Eq. (3)). From the study of the effect of SiH4 partial pressure on the Si nanowire growth rate, the growth rate was found to increase linearly as the SiH4 partial pressure increased from 0.13 to 0.65 Torr. At low SiH4 partial pressures, the Si nanowire growth rate can be assumed to follow a first-order dependence with respect to SiH4 partial pressure: Growth rate ¼ kPSiH4 :

ð4Þ

Using the data in Figs. 6 and 7, an expression for the rate constant of reaction (3) was determined, where  mm  k ¼ 1:38 106 min Torr   22 kcal=mol exp : ð5Þ RT The nanowire growth rates measured in this study are in the range of those previously reported for Si VLS growth. The growth rate of Si nanowires on a Si substrate via VLS growth was reported to be 9.0 103 mm/min at 520 C and a low SiH4 partial pressure of 0.01 Torr [12]. Based on Eq. (5), a growth rate of approximately 1.19 102 mm/min would be predicted at 520 C and a SiH4 partial pressure of 0.01 Torr, which is similar to the reported experimental results. These results demonstrate that the simple heterogeneous reaction model developed in this work is useful for predicting the growth rate of silicon nanowires via VLS growth from a SiH4 source for both template and surface grown nanowires.

6. Conclusions The effect of reaction conditions on the growth rate of Si nanowires via template-directed VLS growth from a SiH4 source was investigated. The Si nanowire growth rate follows an Arrhenius relation over the temperature range of 400–500 C with an activation energy of 22 kcal/mol. Decomposition of SiH4 through deposition of Si on the membrane surface and pore walls was observed when the temperature was greater than 500 C. The activation energy is considered to be associated

22

K.-K. Lew, J.M. Redwing / Journal of Crystal Growth 254 (2003) 14–22

with the heterogeneous decomposition of SiH4 on the Au–Si liquid surface, which is assumed to be the rate-limiting step in the growth process. Based on these results, a heterogeneous reaction model was developed to predict the nanowire growth rate as a function of temperature and SiH4 partial pressure and was found to be useful in predicting nanowire growth rates for both template-directed and conventional VLS growth from a surface.

Acknowledgements This work was supported by the National Science Foundation under grant number DMR0103068 and The Pennsylvania State University Materials Research Science and Engineering Center (MRSEC) on Collective Phenomena in Restricted Geometries.

References [1] S. Iijima, Nature 354 (1991) 56. [2] Y. Cui, Q. Wei, H. Park, C.M. Lieber, Science 293 (2001) 1289. [3] M.S. Gudiksen, L.J. Lauhon, J. Wang, D.C. Smith, C.M. Lieber, Nature 415 (2002) 617. [4] R.S. Wagner, W.C. Ellis, Appl. Phys. Lett. 4 (1964) 89. [5] R.S. Wagner, W.C. Ellis, K.A. Jackson, S.M. Arnold, J. Appl. Phys. 35 (1964) 2993. [6] Y. Okajima, S. Asai, Y. Terui, R. Terasaki, H. Murata, J. Crystal Growth 141 (1994) 357. [7] Y. Okajima, M. Amemiya, K. Kato, S. Asai, J. Crystal Growth 165 (1996) 37. [8] A.M. Morales, C.M. Lieber, Science 279 (1998) 208.

[9] D.P. Yu, Z.G. Bai, Y. Ding, Q.L. Hang, H.Z. Zhang, J.J. Wang, Y.H. Zou, W. Qian, G.C. Xiong, H.T. Zhou, S.Q. Feng, Appl. Phys. Lett. 72 (26) (1998) 3458. [10] Y. Cui, L.J. Lauhon, M.S. Gudiksen, J. Wang, C.M. Lieber, Appl. Phys. Lett. 78 (15) (2001) 2214. [11] J. Westwater, D.P. Gosain, S. Tomiya, Y. Hirano, S. Usui, H. Ruda, Mat. Res. Soc. Symp. Proc. 452 (1997) 237. [12] J. Westwater, D.P. Gosain, S. Tomiya, S. Usui, H. Ruda, J. Vac. Sci. Technol. B 15 (3) (1997) 554. [13] K.-K. Lew, C. Reuther, A.H. Carim, J.M. Redwing, J. Vac. Sci. Technol. B 20 (2002) 389. [14] A.H. Carim, K.-K. Lew, J.M. Redwing, Adv. Mat. 13 (2001) 1489. [15] D. Routkevitch, J. Chan, J.M. Xu, M. Moskovits, Electrochem. Soc. Proc. 97 (1997) 350. [16] B.R. Martin, D.J. Dermody, B.D. Reiss, M. Fang, L.A. Lyon, M.J. Natan, T.E. Mallouk, Adv. Mater. 11 (1999) 1021. [17] E. Fitzer, W. Fritz, G. Schoch, J. Phys. IV 1 (C2) (1991) 143. [18] H.K. Moffat, K.F. Jensen, J. Electrochem. Soc. 135 (1988) 459. [19] D.W. Foster, A.J. Learn, T.I. Kamins, J. Vac. Sci. Technol. B 4 (5) (1986) 1182. [20] W.A.P. Claassen, J. Bloem, W.G.J.N. Valkenburg, C.H.J. Van Den Brekel, J. Crystal Growth 57 (1982) 259. [21] G.A. Bootsma, H.J. Gassen, J. Crystal Growth 10 (1971) 223. [22] E.I. Givargizov, J. Crystal Growth 31 (1975) 20. [23] V.M. Glazov, L.M. Pavlova, K.V. Rezontov, Russian J. Phys. Chem. 71 (5) (1997) 738. [24] D.R. Poirier, G.H. Geiger, Transport Phenomena in Materials Processing, USA, 1994. [25] B.S. Meyerson, J.M. Jasinski, J. Appl. Phys. 61 (2) (1986) 785. [26] J.P. Hirth, G.M. Pound, J. Phys. Chem. 64 (1960) 619.