Taguchi analysis of parameters for small-diameter single wall carbon nanotube growth

Small diameter single wall carbon nanotubes are desirable for various physical and electrical properties of carbon nanotubes. Here, we report the sensitivities of parameters and the optimal conditions for small diameter carbon nanotube growth by chemical vapor deposition (CVD). These results were obtained using the Taguchi method, which is commonly used to find the optimal parameters of various processes. The possible parameter ranges given by the experimental equipment and laboratory conditions, we attempted several times to determine the proper ranges, using photoluminescence (PL) imaging to determine the exact positions of suspended carbon nanotubes on the quartz substrates after synthesis. The diameters of the carbon nanotubes were then determined from the radial breathing modes (RBM) using Raman spectroscopy with a 785nm wavelength laser. Among the 4 major parameters listed above, we concluded that the temperature was the most significant parameter in determining carbon nanotube diameter, hydrogen fl...


I. INTRODUCTION
Carbon nanotubes have been widely researched since their discovery in 1991 by Iijima. 1 During this time, carbon nanotubes (CNTs) have been utilized for a variety of applications.For several applications, such as short wavelength emission, CNTs with small diameters are needed.The electronic structure of carbon nanotubes is strongly dependent on their diameter. 28][9] The previous research of Arjmandi et al. investigated chemical vapor deposition (CVD) synthesis of carbon nanotubes based on equipment designed and developed within their group. 10While these studies report various recipes of how to make small diameter nanotubes, they do not investigate the sensitivities of each growth parameter for SWNTS with small diameter.In this paper, we report the sensitivities of these growth parameters for making SWNTs with small diameters.

II. EXPERIMENTS
In the work reported here, quartz pillars (2µm wide and 8µm deep) are fabricated using photolithography and deep reactive ion etching (DRIE).Prior to etching, we use electron-beam evaporation to deposit Fe catalyst (1-2nm in thickness) on top of the quartz pillars.Figure 1 shows optical microscope and scanning electron microscope (SEM) images of these pillars with suspended carbon nanotubes.Our reaction chamber consists of a quartz tube furnace, 70cm in length and 2.5cm in diameter. 11The four major parameters of the synthesis of SWNTs are growth temperature, growth time, ethanol and argon gas flow rate, and hydrogen flow rate.Within the possible parameter ranges, which were given by equipment and laboratory conditions, we made several attempts to establish the proper ranges.PL imaging was carried out using a thermoelectrically cooled InGaAs array (Xenics, Inc.) in conjunction with a defocused 785nm laser.These images were used to identify the exact positions of these suspended SWNTs, and the radial breathing mode (RBM) frequency was measured by Raman spectroscopy to determine the diameter of each SWNT.The RBM was typically observed in the range between 100 to 250 cm -1 .
The initial parameters of the growth conditions are listed in Table I.Several growths were carried out under a wide range of conditions in order to establish the relatively narrow ranges listed in Table II.3][14][15] According to the 3 levels for each of the four main growth parameters, we chose the Taguchi L 9 orthogonal array design listed in Table IV. 16,17

III. RESULTS AND DISCUSSIONS
PL imaging was used to find the exact positions of the CNTs on the quartz pillars.Raman spectra were then collected using a 785nm wavelength laser in order to determine the diameters of the suspended CNTs.The diameter of SWNTs is inversely proportional to the frequency of the RBM,  according to the following relation: [18][19][20] ω RBM = 227cm −1 • nm d The average Raman shifts observed for set of growth conditions are listed in Table V.We analyzed the sensitivities in Table VI using the Taguchi method.
Here, the large values of the RBM frequency are better, since they correspond to smaller diameter nanotubes.We found the optimal configuration to grow small diameter SWNTs to be A 3 B 3 C 1 D 2 , corresponding to configuration No. 9.In this configuration, the temperature was 840 • C, the time was 4m30s, the ethanol and argon gas flow rate was 0.13slm, and the hydrogen flow rate was 0.1slm.Figure 2 plots the average radial breathing mode (RBM) frequency obtained for each growth parameter.In the Taguchi analysis, we used the criterion that larger RBM (i.e., smaller diameter) nanotubes are more desirable.The average RBM Raman shift obtained with A 3 B 3 C 1 D 2 was 219cm -1 .Based on the following equation we obtained a diameter of d = 1.04 nm for these nanotubes.
Figure 3 shows the temperature was the most significant parameter yielding a 43.6% change in the average RBM frequency, hydrogen flow rate was the second most significant parameter with a 40.5% change, the next is ethanol and argon gas flow rate with 13.7%, and the growth time was the least significant parameter with only 2.1% change in the RBM frequency under the above parameter ranges.This means that we must adjust the temperature and hydrogen only to make SWNTs with small diameters, and we can neglect the ethanol and argon gas flow rate, as well as the time parameter.
In order to verify and compare with the above results, we synthesized CNTs with the A 3 B 2 C 2 D 1 combination, which is not optimal but is a relatively effective combination for growing SWNTs with small diameter.According to the results above, an average RBM 11.2% less than that produced under the optimal conditions (i.e., A 3 B 3 C 1 D 2 ) is considered good under the Taguchi analysis.We compared the optimal combination results (A 3 B 3 C 1 D 2 ) with the initial combination (A 2 B 2 C 2 D 2 ) as listed in Table I.Here, the optimal combination produced considerably smaller diameter nanotubes than the initial combination by 23.8%.FIG. 2. Average radial breathing mode (RBM) frequency obtained for each growth parameter.In the Taguchi analysis, we used the criterion that larger RBM (i.e., smaller diameter) nanotubes are more desirable.

IV. CONCLUSION
In this study, we quantitatively investigated the sensitivities of four main parameters in the growth of small diameter SWNTs using the Taguchi method.Here, the tests were conducted over a range of the 4 major growth parameters, which include temperature, time, ethanol and argon gas flow rate, and hydrogen gas flow rate.From this analysis, we conclude which of these parameters were the most significant for synthesizing small diameter SWNTs.Among the 4 parameters listed above, the temperature was the most significant parameter, hydrogen flow rate was the second most significant, ethanol and argon gas flow rate was the third, and finally time was insignificant parameter, indicating that we can neglect the time parameter.

FIG. 3 .
FIG. 3. Raman spectra of suspended carbon nanotubes grown using configuration No. 9 A 3 B 3 C 1 D 2 .The orange and blue curves show spectra from different suspended CNTs.

TABLE I .
Initial growth combination.

TABLE III .
Taguchi L 9 orthogonal array design.

TABLE V .
Average Raman Shifts.

TABLE VI .
Sensitivities of each growth parameters.