Self-similar organization of arrays of individual carbon nanotubes and carbon nanotube micropillars

Self-similar organization of arrays of individual carbon nanotubes and carbon nanotube micropillars

Microelectronic Engineering 87 (2010) 1233–1238 Contents lists available at ScienceDirect Microelectronic Engineering journal homepage: www.elsevier...

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Microelectronic Engineering 87 (2010) 1233–1238

Contents lists available at ScienceDirect

Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee

Self-similar organization of arrays of individual carbon nanotubes and carbon nanotube micropillars Michaël F.L. De Volder a,b,c,*, Daniel O. Vidaud a, Eric R. Meshot a, Sameh Tawfick a, A. John Hart a,* a

Mechanosynthesis Group, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA IMEC Belgium, Kapeldreef 75, 3001 Leuven, Belgium c Division PMA, Department of Mechanical Engineering, KULeuven, Celestijnenlaan 300B, 3001, Leuven, Belgium b

a r t i c l e

i n f o

Article history: Received 14 September 2009 Received in revised form 2 November 2009 Accepted 25 November 2009 Available online 29 November 2009 Keywords: Carbon nanotube CNT Self-organization Microstructure CVD

a b s t r a c t It is well-known that carbon nanotube (CNT) growth from a dense arrangement of catalyst nanoparticles creates a vertically aligned CNT forest. CNT forests offer attractive anisotropic mechanical, thermal, and electrical properties, and their anisotropic structure is enabled by the self-organization of a large number of CNTs. This process is governed by individual CNT diameter, spacing, and the CNT-to-CNT interaction. However, little information is known about the self-organization of CNTs within a forest. Insight into the self-organization is, however, essential for tailoring the properties of the CNT forests for applications such as electrical interconnects, thermal interfaces, dry adhesives and energy storage. We demonstrate that arrays of CNT micropillars having micron-scale diameters organize in a similar manner as individual CNTs within a forest. For example, as previously demonstrated for individual CNTs within a forest, entanglement of small-diameter CNT micropillars during the initial stage of growth creates a film of entwined pillars. This layer enables coordinated subsequent growth of the pillars in the vertical direction, in a case where isolated pillars would not grow in a self-supporting fashion. Finally, we provide a detailed overview of the self-organization as a function of the diameter, length and spacing of the CNT pillars. This study, which is applicable to many one-dimensional nanostructured films, demonstrates guidelines for tailoring the self-organization which can enable control of the collective mechanical, electrical and interfacial properties of the films. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Carbon nanotubes (CNTs) have been studied extensively because of their outstanding electrical, mechanical and thermal properties [1]. A common way to integrate CNTs in electrical devices and other microsystems is to ‘‘grow” them from an arrangement of metal ‘‘catalyst” nanoparticles using thermal Chemical Vapor Deposition (CVD) [2]. This process typically results in arrays of self-assembled, vertically aligned CNTs also referred to as ‘‘CNT forests” [3]. Although this method is well established, the exact mechanisms behind the self-organization of the CNTs into vertically aligned super-structures remain unclear. Insight into the self-organization is important in order to tailor the properties of the CNT forests towards certain applications, such as electrical interconnects [1,4], dry adhesives [5], energy storage [6] and thermal interfaces [7].

* Corresponding authors. Address: IMEC Belgium, Kapeldreef 75, 3001 Leuven, Belgium. E-mail addresses: [email protected] (M.F.L. De Volder), ajohnh@umich. edu (A.J. Hart). 0167-9317/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2009.11.139

The ability of CNTs to self-organize into vertically aligned forests depends on their diameter and spacing, as well as the surface interactions between individual CNTs; this, in turn, affects the collective properties of the CNT assembly. For example, relatively thick CNTs or carbon nanofibres (50 nm diameter) grown by plasma enhanced CVD can typically grow straight and self-standing up to lengths of approximately 10 lm [8]. Above these lengths, individual CNTs are unable to grow straight, so they bend or fall over. However, within CNT forests, individual CNTs self-organize and support each other to grow vertically up to lengths of several millimeters [3,9,10]. Forests typically have a density of 1010–1013 CNTs per square centimeter [11,12], meaning that each square micrometer of CNT forest contains thousands of self-organized CNTs. As previously reported by several authors, another crucial factor in the growth and organization of individual CNTs is the formation of an initial entangled CNT film [13,14]. This ‘‘crust” layer enables coordinated subsequent growth of the CNTs in the vertical direction in a case where isolated CNTs would not grow in a selfsupporting fashion. The investigation of the self-organization of CNTs and the parameters that influence it are particularly difficult. This is due to the nanoscale nature of the CNT building blocks and the

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Fig. 1. Illustration of the self-similar organization of individual CNTs and CNT pillars.

extreme growth conditions to which they are subject (high growth rate, temperature, plasma, etc.). For instance, deterministic positioning of the nanoscale catalyst particles or highly precise control of the CNT diameter is challenging, especially in the case of small-diameter single-wall nanotubes (SWNTs). In this paper, we propose that arrays of CNT micropillars (each consisting of thousands of CNTs) organize in a similar manner as individual CNTs within a CNT forest as illustrated in Fig. 1. The self-similar behavior provides a powerful tool to investigate the self-organization of CNTs: micrometer-sized pillars are easily controlled in dimensions using lithographic processes. Obviously, the behavior of the micrometer-scale pillars will defer from that of individual nanotubes, but they still allow the investigation of certain trends. More precisely, we characterize the self-organization process of arrays of CNT micropillars as a function of their diameter, length and spacing. 2. Methods CNT forest micropillars are grown on thermally-oxidized (100) silicon wafers on which a 10 nm Al2O3 and 1 nm Fe catalyst layer are sequentially deposited by e-beam evaporation [10]. The catalyst layer is patterned by a lift-off process using photoresist (SPR 220) and ultrasonic agitation in acetone. Next, CNTs are grown in a horizontal tube furnace (22 mm inner diameter, 300 mm heated length) at atmospheric pressure with flows of 100/400/100 sccm C2H4/H2/He, at 775 °C. The initial growth rate is typically 100 lm/min and the growth time is chosen as 0.5–25 min depending on the desired forest height. These growth conditions result in vertically aligned CNT forests, but like most microstructures, the aspect ratio of these structures is limited by internal stresses and other non-uniformities within the pillars. In this case, CNT micropillars with an aspect ratio of more than 8, tend to bend over. In this work, we aim at using CNT micropillars (each an individual ‘‘forest”) as a tool to investigate CNT self-organization process (see Fig. 1). Accordingly, we study arrays of CNT forests with varying diameter, height, and spacing. This arrangement of the CNT forests will be described by defining different ‘‘phases” as illustrated in Fig. 2.

Fig. 2. (a) Phase 1: Straight micropillar growth. (b) Phase 2: Self-supporting micropillars with tip deflections at least one-diameter. (c) Phase 3: Micropillars are touching each other (d) Phase 4: Microstructures self-organize in a super-structure. (e) Phase 5: No vertical growth; structures fall over.

 Phase 3: The micropillars deflect, and adjacent CNT pillars are touching each other.  Phase 4: The CNT pillars are entwined and supporting each other in order to grow vertically as illustrated in Fig. 2.  Phase 5: Micropillars that fail to grow vertically and form a tangled arrangement that remains close to the silicon substrate, whether they are touching one another or not.

3. Results As discussed above, the diameter, length and spacing of CNT micropillars influence their self-organization or their ‘‘phases”. Fig. 3 shows the growth of 5 lm diameter CNT pillars as a function of their spacing and the growth time, while Fig. 4 shows exactly the same experiments for pillars with a diameter of 10 lm. In what follows, the influence of the geometry of pillar array on the self-organization is discussed. 3.1. Influence of the micropillar spacing

 Phase 1: The CNT micropillars grow straight vertically and have tip deflections of less than one time their own diameter, and the pillars are not touching (i.e., are individually self-supporting).  Phase 2: The micropillars have tip deflections of at least one time their own diameter but are self-supporting (i.e., adjacent microstructures are not touching).

As can be seen in both Figs. 3 and 4, the spacing between the CNT pillars has a major influence on the self-organization of these micropillars. First of all, none of the 100 lm spaced pillars formed a super-structure. However, for instance, the rows of 25 min growth in (Fig. 3) and 10 min in Fig. 4, show that pillars with the same

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Fig. 3. SEM images of CNT pillars with 5 lm diameter as a function of the spacing and the growth time (main image scale bars 100 lm).

diameter almost grow perfectly vertically if they are spaced less than 10 lm from each other. Note that this spacing is in the same order of magnitude as the pillar diameter. In both cases, there is also a clear distinction between randomly organized CNT pillars at 30 lm spacing and good vertical alignment below 10 lm. We therefore assume that also within CNT forests, a certain threshold of CNT density needs be achieved in order for the CNTs to form vertically aligned forests. Interestingly, this is also demonstrated for individual CNTs within a forest [12]. Further, the spacing of the pillars also has an influence on the growth rate. The row of 0.5 min growth in Fig. 3 clearly shows no CNT growth at 100 and 30 lm spacing, while pillars placed 10 lm or closer to each other clearly grow. This is could be due to loading effects during the CNT growth process [15]. 3.2. Influence of the micropillar length The aspect ratio of the CNT pillars is obviously limited, here, CNT pillars with an aspect ratio above 8 tend to bend, and at higher aspect ratios, the pillars fall over. Therefore, we normally expect only relatively short CNTs grow vertically. There are, however, two exceptions. The first is the case where the CNTs are packed closely together and therefore force each other to grow straight as discussed above. A second exception is the case where the pillars form

a crust of entangled nanotubes that enables subsequent vertical growth. This is clearly illustrated in the columns of 10 lm spacing in Fig. 3: After 0.5 min, the CNTs grow straight, because the aspect ratio is still below 8. After 1 min, the pillars are too long to remain straight, and fall over, creating a layer of entwined CNT pillars. As the CNTs continue growing, this entangled layer is pushed up because new CNT material is formed at the base of the pillars. The newly formed CNT material is now growing vertically due to the support of the entangled layer as shown in the 10 lm spacing column of Fig. 3 after 3 min. Fig. 5 also shows a clear formation of an entangled crust layer that resides on the top of the super-structures. Interestingly, the formation of entangled crusts is also a well-known phenomenon in the self-organization of individual CNTs within a CNT forests [13] as illustrated in Fig. 5. This again illustrates the self-similar behavior of CNT micropillar arrays and the individual CNTs within a CNT forest. The crust allows the CNT micropillars to achieve subsequent aspect ratios of more than 10, which is higher than without forming the crust layer first. 3.3. Influence of the micropillar diameter Figs. 3 and 4 show the same experiments for pillars with a diameter of 5 lm and 10 lm respectively. As expected, thicker tubes are stiffer, and therefore more readily self-organize into

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Fig. 4. SEM images of CNT pillars with a diameter of 10 lm as a function of the spacing and the growth time (main image scale bars 100 lm).

vertically aligned structures. In order to give a more detailed overview of the influence of the diameter, the above experiments have also been repeated for pillars with a diameter of 5, 10, 30, 100 and 300 lm. These experiments are summarized in Fig. 6 by making use of the above defined phases. These graphs also clearly show how pillars with a large diameter yield better alignment. 4. Discussion The experiments described above show that, to a certain extent, the growth of arrays of CNT micropillars behaves in a similar fashion as individual CNTs. Although the scale and the forces acting on micropillars are obviously different from those acting on individual CNTs, there are a number of physical motivations for this self-similar behavior. To construct quantitative comparisons for the interactions between two CNTs and between two micropillars (comprised of constituents CNTs), we derive the force laws for these systems, recognizing that van der Waals forces play a central role in the physics of interacting bodies since these forces are present at all scales. From the work of Israelachvili [16], we consider an interatomic van der Waals pair potential of the form: Fig. 5. Formation of entangled crust layers on CNT forests (top) and on arrays of CNT micropillars (bottom).

wðrÞ ¼ C=r 6 ;

ð1Þ

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100 d

F/L [ µ N/m]

80 L

60

D

40 20 0 0

2

4

6

8

10

D/d Fig. 7. Calculated van der Waals forces between two parallel cylinders of equal diameter d, separated by a distance D. The force per length is calculated for a range of D values, normalized by d, for each case: pair of parallel CNTs (gray) and pair of parallel CNT micropillars (black).

tions of many CNTs among pillars are governed by a 1=r3=2 potential, which does not decay as rapidly. Simply treating the pillars as solid cylinders with interatomic potentials does not accurately describe the physics and thus does not reveal the correct scaling behavior. The total interaction between two pillars is calculated numerically, assuming an individual CNT diameter of 10 nm and a pillar diameter of 10 lm with a packing fraction of 0.016 which we previously measured for our CNT forests [17]. The van der Waals force (F ¼ @W=@D) between two pillars is presented in Fig. 7 (black) along with the result for two individual CNTs (gray), versus separation distance normalized by the diameter of the respective body. Importantly, both curves show similar interaction forces throughout a wide range of normalized spacing. This self-similar behavior suggests that van der Waals forces could be responsible for the observed similarity in self-organization even for various scales. When a CNT or micropillar is bent due to lateral forces, an elastic force resists the deformation. Accordingly, we show that individual CNTs and CNT pillars have approximately the same bending stiffness: 4

k¼ Fig. 6. Organization of CNT pillars as a function of their diameter for 1, 5 and 15 min growth.

where C represents the strength of the dispersion interaction between spherical, non-polar molecules, and r is the interatomic separation. We model two vertically aligned CNTs as parallel, solid cylinders of equal diameters, so summing the force law of Eq. (1) for each atomic interaction between CNTs gives a van der Waals energy dependence of 1=2

WðDÞ ¼

ALd pffiffiffi : 24 2D3=2

ð2Þ

Here, A is the conventional Hamaker constant, which equals p2 C q2 for two bodies of equal density (1019 J for condensed phases); L is the length of CNTs in contact; d is the diameter of the CNTs; and D is the separation distance of the two CNTs. This result is useful when calculating the interaction of two micropillars of constituent CNTs because we sum the interactions of individual CNTs between micropillars using Eq. (2), where D now represents the spacing between one CNT and another CNT in the second pillar. Applying this potential is a particularly important consideration since at large distances the interatomic potential is negligible (1=r 6 ), whereas the interac-

3pEd

64L3

;

ð3Þ

where E is the effective Young’s modulus, d and L are as defined above. The similarity in stiffness arises because E of CNT pillars is much lower than that of individual CNTs. The bulk Young’s modulus of the CNT pillars depends on the CNT diameter and spacing, and it is low compared to that of individual CNTs due to the very low packing fraction of CNTs within the pillars. For instance, a 10-nmdiameter, 100-nm-long CNT with E = 1 TPa has approximately the same bending stiffness as a 10-lm-diameter, 100-lm-long CNT micropillar with E = 54 MPa. The value of 54 MPa was measured by compression testing of as-grown CNT pillars using a nanoindentation machine. In other words, a CNT pillar that is about 1000 times larger in diameter and length than individual CNTs has approximately the same bending stiffness. Further, the forces acting between two bodies are not sufficient to induce bending in the structures at equilibrium separation distances (D/d  1–10) since the force required to bend a cylindrical cantilever having the dimensions introduced above is as much a 4 lN. However, differential growth rates among CNT populations can induce bending, bringing structures close and into contact with each other, at which point (D/d < 0.1) the van der Waals force is substantial and can maintain coupling between structures. This physical motivation and analysis provides insight into the governing mechanisms of organization of one-dimensional struc-

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tures, and provides an initial clarification for the self-similar behavior of CNTs observed experimentally in this study. 5. Conclusions It is well-known that carbon nanotube (CNT) growth from a dense arrangement of catalyst nanoparticles creates a vertically aligned CNT forest. This vertical growth of tall CNT forests is only possible due to self-organization of the thousands or millions of CNTs that constitute a forest. This paper shows how the self-organization of CNTs within a CNT forest can be studied by using micron-sized CNT pillars. Due to the similar van der Waals interactions and bending stiffness of individual CNTs and the micropillars, and the fact that both are fabricated by the same growth dynamics, they exhibit similar properties. This self-similar behavior is particularly interesting since the shape and spacing of micropillars is much easier to control than that of individual CNTs. We provided a detailed overview of the self-organization as a function of the diameter, length and spacing of the CNT structures. This study is not only applicable to CNTs but also to other one-dimensional nanostructures, and has applications spanning the fields of electrical interconnects, thermal interfaces and the fabrication of MEMS structures. Acknowledgments The authors thank M. Bedewy for assistance with Fig. 5. This research was supported by the College of Engineering and Department of Mechanical Engineering at the University of Michigan,

and the Belgium Fund for Scientific Research–Flanders (FWO). Microfabrication was performed at the Lurie Nanofabrication Facility at the University of Michigan, which is supported by the National Science Foundation through the National Nanotechnology Infrastructure Network. Electron Microscopy was performed at the Michigan Electron Microbeam Analysis Laboratory.

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