Growth Kinetics of Wall-Number Controlled Carbon Nanotube Arrays

Feb 5, 2010 - 2.32 × 109 atoms/s. The rate constants ksb, kc, and kt can be expressed as5 where Esb, Ec, and Eb are the activation barriers associate...
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J. Phys. Chem. C 2010, 114, 3454–3458

Growth Kinetics of Wall-Number Controlled Carbon Nanotube Arrays Duck Hyun Lee, Sang Ouk Kim,* and Won Jong Lee* Department of Materials Science and Engineering, KAIST 373-1, Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea ReceiVed: December 8, 2009; ReVised Manuscript ReceiVed: January 18, 2010

We present a simple model for the growth and termination of carbon nanotube (CNT) arrays. This model was developed by modifying several submodels and provides a comprehensive predictive tool for the CNT growth process as a function of CNT wall number. Wall number, diameter, and areal density-controlled CNT arrays were grown on a reduced graphene film by combining block copolymer lithography and plasmaenhanced chemical vapor deposition (PECVD) method. The number of carbonaceous platelets required for the termination of CNT growth process was measured by high-resolution transmission electron microscopy (HRTEM), and the effective exposed catalyst surface area was measured by high magnification scanning electron microscopy (SEM). A parametric study showed that our simple kinetic model successfully predicted the kinetics of wall number-dependent CNT growth and could be used to optimize the PECVD process for CNT production. 1. Introduction Vertically aligned carbon nanotube (CNT) arrays grown on conductive substrates are attractive for use in technological applications, such as electron emitters, gas sensors, and nanoelectronic devices.1–3 Several intensive research efforts have sought to optimize the growth process and model the growth kinetics of these arrays.4–9 Catalytic growth of vertical CNT arrays using chemical vapor deposition (CVD), which is a facile and scalable process, has become standard.10 Plasma-enhanced CVD (PECVD) is particularly attractive, because the highenergy plasma environment allows low-temperature growth, produces a high degree of CNT alignment, and is compatible with conventional Si processing techniques. In a typical CVD process, metal particles on a substrate surface are used to catalyze the vertical growth of CNT arrays. The physical properties of CNT nanostructured arrays (e.g., wall number, diameter, and center-to-center distance) are determined by the size and lateral distribution of catalyst particles. Preparation of an array of uniformly sized and laterally distributed catalyst particles over a large surface area provides a means for controlling the properties of CNT arrays. Researchers have reported several optimized parameters for CVD processes, such as catalyst quantity, preparation of the supporting substrate, composition of the reaction gas, gas flow rates, and growth temperature, which can dramatically affect the yield and quality of CNT arrays. Although empirical models of growth kinetics have been reported, a clear explanation for the growth and termination kinetics of CNT arrays has been lacking.5,7,8 The use of polydisperse catalyst particles contributes to uncertainty in theoretical models. Conventionally, catalyst particles have been prepared by depositing a thin catalyst film onto a substrate, followed by heat treatment. The deposited film dewetted under heat treatment to form catalyst particles.11,12 The prepared catalyst particles were polydisperse in size and were randomly distributed over the substrate surface, making it * Corresponding authors. (W.J.L.) E-mail: [email protected]. Phone: +82-42-350-4217. Fax: +82-42-350-3310. (S.O.K.) E-mail: sangouk. [email protected].

difficult to achieve reproducible growth of CNT arrays for a given set of process parameters. These problems limited the practical application of CNT arrays and hindered the development of theoretical frameworks that described the array growth and termination kinetics. Recently, we described the reproducible (with respect to wall number, diameter, and areal density) growth of CNT arrays by combining block copolymer lithography13–16 and PECVD methods.17–21 Here, we present a model for the growth and termination of CNT arrays that predicts the physical properties of the product array as a function of wall number. For the precise evaluation of this model, the number of carbonaceous platelets and the effective surface area of the exposed catalyst were measured by SEM and TEM, respectively. We present a comparison of the predicted array properties and the experimental results (wall number-dependent CNT length) as a function of time, to evaluate the validity of the proposed kinetic model. 2. Experimental Details 2.1. Materials. An asymmetric block copolymer, PS-bPMMA, which forms cylindrical nanostructures (molecular weight: PS/PMMA-46k/21k), was purchased from Polymer Source Inc. The iron source for E-beam evaporation (purity: 99.95%) was purchased from Thifine. Pure oxygen, hydrogen, and acetylene gases were purchased from Kyungin Chemical Industrial. 2.2. Nanopatterned Catalyst Particle Preparation. An aqueous dispersion of graphite oxide was prepared using methods described elsewhere.21–23 A film composed of overlapped and stacked graphene oxide platelets was prepared by spin-coating the aqueous dispersion onto a SiO2 (500 nm)/Si wafer. The graphene oxide surface was neutrally treated by a random copolymer brush. A thin film (thickness: 42 nm) of the block copolymer, polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA, molecular weight: PS/PMMA-46k/21k), was spin-coated onto the wafer surface. After high temperature annealing at 250 °C, the substrates were rinsed with acetic acid and water. The washes removed the PMMA cylinder cores and

10.1021/jp911629j  2010 American Chemical Society Published on Web 02/05/2010

Wall-Number Controlled CNT Arrays cross-linked the PS matrix. The substrate was exposed to oxygen plasma for 20 s to remove the remnant cylinder cores. An iron catalyst film was deposited (thickness: 10-0.7 nm) onto the block copolymer template by tilted evaporation (tilt angle: 0°-30°).19 After the deposition process, the remaining PS nanoporous template was lifted off by sonication in toluene. 2.3. CVD Growth of Vertical CNT Arrays. CNT growth was carried out on the prepared substrates by PECVD. The substrate was heated to 600 °C under the flow of a C2H2/H2/ NH3 (5 sccm/80 sccm/20 sccm) gas mixture. When the substrate temperature reached 600 °C, the chamber pressure was adjusted to 5 Torr, and application of 470 V DC power produced the plasma. Slow streaming of acetylene gas resulted in the growth of vertical CNT arrays (growth time: 0-15 min.). The lengths of CNTs in the resultant arrays were measured from SEM crosssectional images. The diameters of the CNTs and the catalyst particles as well as the contact angle between the iron catalyst and substrate surface were measured from 30 randomly chosen CNT-catalyst high-resolution cross-sectional SEM images. 2.4. Quantification of the CNT Wall-Number and the Carbonaceous Layers. The CNT wall-number and the number of carbonaceous layers on the surface of each catalyst particle, after termination of CNT growth, was measured by TEM. TEM samples were prepared as follows. As-grown CNTs were detached from the catalyst particle. The adhesion between CNT and catalyst particle was weak, allowing the CNT arrays to be easily detached from the surface of the catalyst particles. The detached CNTs were ultrasonically dispersed in ethanol. A drop of the CNT dispersion was deposited onto a carbon supported TEM grid and air-dried. For statistical analyses, the wall number of 100 randomly chosen CNTs was measured from the TEM images. The catalyst particles attached to the reduced graphene film were exfoliated from the SiO2 wafer by razoring the surface of wafer. Ultrasonication facilitated the detachment and dispersal of individual catalyst particles from the surface of the reduced graphene film. The solution containing the dispersed reduced graphene dispersion was deposited dropwise onto the carbon supported TEM grid and air-dried. For statistical analyses, the number of carbonaceous layer of 30 randomly chosen catalyst particles was measured from the TEM images. 3. Results and Discussion 3.1. CNT Array Growth Kinetics. The kinetics model for the growth and termination of CNT arrays was developed from previously described CNT growth models5 and includes additional descriptions of the dependence of the termination length on the size of the catalyst particles and the wall number of CNTs. Generally, the catalyzed growth of CNT arrays using CVD methods is assumed to occur via a three-step process:5–7 (i) surface adsorption of carbon atoms from the carboncontaining feed gas, (ii) diffusion of the adsorbed carbon atoms through the bulk metal catalyst, and (iii) the growth of CNTs through formation of a graphene layer from the diffusing carbon atoms. Growth is terminated by the formation of a carbonaceous platelet on the surface of the catalyst particles, which limits the subsequent adsorption of carbon atoms. As the CNT growth mechanism of PECVD process is the same with the thermal CVD process, it also can be applied to the PECVD process. The scheme shown in Figure 1 describes the kinetic model for growth and termination of CNT arrays grown by the base growth mode. The kinetics of CNT array growth and termination, discussed above, can be described by the following set of differential equations:5

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(

)

(1)

dNL(t) ) kcNC(t) dt

(2)

dNB(t) ) ksbNC(t) - ktNB(t) dt

(3)

dNT(t) ) ktNB(t) dt

(4)

dNC(t) NL(t) - ksbNC(t) - kcNC(t) ) Fc,adsA0 1 dt A0Rnm

where NC is the number of carbon atoms (produced by adsorption of the hydrocarbon feed gas, C2H2) on the surface of a catalyst nanoparticle, NL is the number of carbon atoms in the carbonaceous platelet on the surface of the catalyst particle, NB is the number of carbon atoms diffusing within the catalyst particle, NT is the number of carbon atoms in the graphene layers of the CNT, ksb is the rate of diffusion of carbon atoms between the surface and bulk, kc is the rate of formation of carbonaceous platelets, kt is the rate of diffusion from the bulk particle to the growing end of a CNT, nm ) 107 atoms/µm2 is the surface density of carbon atoms in the graphene monolayer, R is the number of carbonaceous platelets on the surface of a catalyst particle, A0 is the initial exposed surface area of a catalyst particle onto which carbon atoms can adsorb, and Fc,ads is the flux density of carbon atoms adsorbed onto the surface of a catalyst particle. This work considered only relatively low (600 °C) CNT growth temperatures; therefore, high temperature effects, such as poisoning due to gas phase pyrolysis products or the formation of iron carbide, which deactivate the catalyst particles, will not be considered. The adsorption rate of carbon atoms (Fc,ads) can be estimated as the product of the flux density of incident molecules (Fc, i) and the sticking coefficient of the carbon-containing feed gas (S). By adapting the Hertz-Knudsen equation, the overall adsorption rate is given by24,25

Fc,ads ) Fc,iS )

jp

√2πmkBT

S

(5)

where j is the number of carbon atoms contained in each molecule of hydrocarbon feed gas (e.g., j ) 2 for C2H2), p is the near-surface partial pressure of the hydrocarbon feed gas, m is the molar mass of the hydrocarbon feed gas, kB is the Boltzmann constant, and T is the gas temperature at the surface of the catalyst particles. In our case, Fc,i is approximately 1.16 × 1012 atoms/s at 600 °C and a C2H2 partial pressure is 0.25 Torr. S ) 0.002, was determined by a fit to the experimental data of 6-walled CNT arrays (Supporting Information, Figure S1). Equation 5 was used to

Figure 1. Illustration of the proposed model for the growth and termination of CNT arrays.

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Lee et al.

calculate an estimate for flux density of incident molecules, Fc,ads ≈ 2.32 × 109 atoms/s. The rate constants ksb, kc, and kt can be expressed as5

( )

ksb ) C1 exp -

Esb , kBT

( )

kc ) C2 exp -

Ec , kBT

( )

kt ) C3 exp -

Et kBT

(6)

where Esb, Ec, and Eb are the activation barriers associated with surface-bulk penetration, formation of the carbonaceous platelet, and diffusion from the bulk to the growing end of a CNT, respectively, and C1, C2, and C3 are the pre-exponential factors. Previous work predicted that ksb and kt are much larger (by a factor of 104) than kc (ksb, kt . kc) for the growth of CNTs.5,6 If kc were comparable in magnitude to ksb and kt, then the carbonaceous platelet would form prior to the growth of CNT arrays, and CNT growth would be terminated. Estimation of ksb and kt was accomplished using the previously reported parameter values5 C1 ) 2.18 × 1014/s, C3 ) 1.0 × 1012/s, Esb ) 2.0 eV, and Et ) 1.5 eV, which yielded in ksb ) 588/s, kt ) 2100/s from eq 6. The rate of formation of carbonaceous platelets, kc ) 0.05/s, was determined by a fit to the experimental data of 6-walled CNT arrays (Supporting Information, Figure S1). Assuming that ksb and kt were much larger than kc (ksb, kt . kc), NB(t) was derived using eqs 1-4

NB(t) )

Fc,adsA0 -(Fc,adskc/Rnmksb)t e kt

Figure 2. HRTEM images of iron catalyst particles coated with the carbonaceous platelets responsible for the growth of (a) 2-walled, (b) 3-walled, (c) 6-walled, and (d) 10-walled CNT arrays. All particles displayed ∼5 layers of carbonaceous platelets (R), regardless of the CNT wall number. HRTEM images of (e) carbonaceous platelets and (f) iron catalyst particles. The interlayer distance of carbonaceous platelets was 0.59 nm.

(7) theoretical eq 9, and the parameters β and τ0 in eq 11 can be expressed in terms of the parameters used in our model:

The time-dependent growth rate and length of CNT arrays, γ(t) and L(t), were estimated as

β)

Fc,adsA0 z

(12)

τ0 )

Rnmksb Fc,adskc

(13)

Fc,adsA0 -(Fc,adskc/Rnmksb)t kt 1 dNT(t) γ(t) ) ) NB(t) ) e z dt z z

(8) L(t) )

NT(t) A0Rnmksb (1 - e-(Fc,adskc/Rnmksb)t) ) z zkc

(9)

where z is the number of carbon atoms in a CNT of length 1 µm. Assuming that the interwall distance between CNTs was fixed at 0.34 nm, z was estimated by

z ) π · nwnm(dn - 0.34 × 10-3(nw - 1))

(10)

where nw and dn are the wall number and the outer diameter of a CNT, respectively. Futaba et al.8 reported that the time-dependent length of CNT arrays can be expressed by the following empirical equation, developed using experimental data from the water-assisted CVD growth of CNTs.

L(t) ) βτ0(1 - e-t/τ0)

(11)

where β is the initial growth rate and τ0 is the characteristic growth time. Interestingly, this equation agreed with our

The above equations describe the initial growth rate (β) as proportional to the product of the flux density of adsorbed carbon atoms (Fc,ads) and the exposed surface area of catalyst particles (A0). This product indicates the total number of carbon atoms supplied for growth. To achieve higher CNT wall numbers and larger diameters, more carbon atoms are required per 1 µm (in length) of CNT growth (corresponding to an increase in z), which decreases the initial growth rate. The characteristic growth time (τ0) is proportional to the layer number of the carbonaceous platelet (R) and to the rate constant for diffusion of carbon atoms between the surface and bulk (ksb). Increasing the wall number of CNTs increases the CNT growth termination time. The characteristic growth time is inversely proportional to both the flux density of adsorbed carbon atoms (Fc,ads) and to the rate constant for formation of the carbonaceous layer (kc), both of which processes promote the formation of carbonaceous platelets. Qualitative analysis of the kinetics model requires a more precise evaluation of R and A0. 3.2. Measurement of the Number of Carbonaceous Platelets, r. The number of carbonaceous platelets formed on the surface of catalyst particles was determined by detaching the reduced graphene film from the SiO2 wafer, followed by TEM

Wall-Number Controlled CNT Arrays

J. Phys. Chem. C, Vol. 114, No. 8, 2010 3457

π(cos θ1 + cos θ2)dc2 A0 ) ) 2

( (

π cos sin-1

Figure 3. (a) High magnification SEM images of 10-walled CNTs grown on iron catalyst particles. (b) The dn/dc ratio plotted as a function of CNT diameter (dn). Inset SEM images compare the ratio of diameters of CNTs (dn) and catalyst particles (dc) for the 2-walled, 3-walled, 6-walled, and 10-walled CNT arrays.

analysis. Figure 2a-d shows HRTEM images of the iron catalyst particles coated with the carbonaceous platelets responsible for the growth of (a) 2-walled, (b) 3-walled, (c) 6-walled, and (d) 10-walled CNT arrays, respectively. All catalyst particles, regardless of size or CNT wall number, featured five layers of carbonaceous platelets (R). Figure 2e shows magnified TEM images of the carbonaceous platelets. The atomic-level structure of the carbonaceous platelets that terminate CNT growth has been the subject of debate.5,7,26,27 We found that the carbonaceous platelets had a graphene-like structure with an interlayer distance of 0.59 nm, which is larger than that of the graphene layer (0.34 nm). Figure 2f shows HRTEM images of iron catalyst particles (a 111 plane with a d-spacing of 0.17 nm). An iron carbide structure was not observed. The iron catalyst particles did not convert into iron carbide during CNT growth because the growth temperature (600 °C) was relatively low, in agreement with the assumptions used in the development of our model. 3.3. Evaluation of Exposed Surface Area, A0. The exposed surface area of a catalyst particle (A0) is an important parameter for the calculation of the total number of supplied carbon atoms, which decides the terminal length of CNT arrays. Figure 3a shows high magnification SEM images of 10-walled CNTs grown on iron catalyst particles. We assume that the catalyst particles are ideally spherical and that the surface areas capped by the CNT growth end and the SiO2 wafer are excluded from the effective surface area of the catalyst particle. The exposed surface area of a catalyst particle (A0) can be estimated by

)

)

dn + cos 78°) dc2 dc 2

(14)

Because θ1 corresponds to the ratio of dn and dc, it can be calculated as sin-1(dn/dc). θ2 is determined by the surface tensions of the catalyst particle and SiO2 substrate. It is independent of the size of the catalyst particle, and was measured, from the high-magnification SEM images, to be 78°. Figure 3b plots the dn/dc ratio as a function of CNT diameter (dn). Inset SEM images compare the ratio of the diameters of CNTs (dn) and catalyst particles (dc) for the various types (2walled, 3-walled, 6-walled, and 10-walled) of CNT array. Previously, Moodley et al.26 reported that the relationship between catalyst particle size and CNT diameter could not be predicted for the ordinary CNT growth method due to the particle rearrangement induced by Oswald ripening during the growth of CNT arrays. However, the patterning of catalyst particles via block copolymer lithographic methods, yielded a center-to-center distance between catalyst particles that was much larger (42 nm) than the separation produced by ordinary CNT growth methods. Larger particle separations prohibited the rearrangement of catalyst particles, and the size of catalyst particles did not change during the CNT growth process. Because the catalyst particles were characterized by a narrow size distribution across the surface of the substrate, the diameters and wall numbers of CNTs in the array were also narrowly distributed, and a correlation between the wall number and outer diameter of CNTs was observed. Figure 4 shows the wall number of the CNT arrays plotted as a function of the CNT outer diameter. A linear fit of the experimental data yielded the

Figure 4. Wall number of CNT arrays plotted as a function of the outer diameter of CNTs. A linear fit of the experimental data yielded the relationship between the wall number and outer diameter of CNTs, dn[µm] ) 0.00142nw + 0.0008.

TABLE 1: List of Parameters Used in the Simulations parameter

value

comments and refs

Fc,I S

1.16 × 1012 atoms s-1 0.002

Fc,ads nm ksb kc

2.32 × 109 atoms s-1 1.0 × 107 atoms µm-2 588 s-1 0.05 s-1

kt θ1 θ2 R

2100 s-1 sin-1(dn/dc) 78° 5

calculated from ref 21 fitted from experimental data of 6-walled CNTs calculated from ref 21 ref 5 calculated from ref 5 fitted from experimental data of 6-walled CNTs calculated from ref 5 experimental data experimental data experimental data

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Lee et al. Initiative (EEWS0903). R.S.R. was supported by NSF Grants #CMMI-0802247 and #CMMI-0742065. Supporting Information Available: Figure S1 showing time-dependent length and growth rate of CNTs. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes

Figure 5. Experimental (dotted) and calculated (lines) time-dependent length of CNTs in the CNT arrays, plotted as a function of the CNT wall number.

following relationship between the wall number and outer diameter of CNTs:

dn[µm] ) 0.00142nw + 0.0008

(15)

3.4. Time-Dependence of CNT Length in CNT Arrays. The above equations allow prediction of the time-dependent length of CNTs in CNT arrays, as a function of CNT wall number. Table 1 lists the parameter values used in the simulations. Figure 5 compares the experimental (dotted) and calculated (lines) lengths of CNTs in arrays, plotted as a function of the CNT wall number. An increase in the wall number increased the terminal length of CNTs in the arrays without affecting the characteristic growth time. For all types of CNT arrays, the calculated time-dependent length of CNT arrays (lines) agreed well with the experimental data (dots) over the course of the growth process. 4. Conclusion In summary, we present a simple model for the growth and termination of CNT arrays, derived by modifying several submodels. This composite model provides a comprehensive approach to the prediction of CNT growth process as a function of CNT wall number. The kinetic model was evaluated experimentally by precisely measuring the number of carbonaceous platelets and the effective exposed catalyst surface area. A parametric study showed that our kinetic model successfully predicts the kinetics of wall number-dependent CNT growth, and can thus be used to identify and optimize CVD process parameters for use in CNT array production. Acknowledgment. This work was supported by National Research Laboratory Program (R0A-2008-000-20057-0), the World Class University (WCU) program (R32-2008- 000-100510), the pioneer research center program (2009-0093758), the Korea Science and Engineering Foundation (KOSEF) Grant (R11-2008-058-03002-0) funded by the Korean government, and KAIST EEWS (Energy, Environment, Water and Sustainability)

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