SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION Flexible, high-performance carbon nanotube integrated circuits Dong-ming Sun, Marina Y. Timmermans, Ying Tian, Albert G. Nasibulin, Esko I. Kauppinen, Shigeru Kishimoto, Takashi Mizutani and Yutaka Ohno Supplementary 1: AFM image of carbon nanotube network and distribution of diameters of nanotubes Figure S1a shows the AFM image of the carbon nanotube network in a TFT on a Si/SiO 2 substrate. In Fig. S1b, the histogram shows the distribution of the diameter of branches in the network. The peak count was obtained for the diameter of around 1 nm, which is almost equal to the diameter of individual nanotubes evaluated from the absorption spectrum shown in the inset. Therefore, the Y-junction network of the present sample can be considered to mainly consist of individual nanotubes, whereas bundles of a few nanotubes exist at some parts. Figure S1. a, AFM image of carbon nanotube network. b, Distribution of diameters of branches in the network. The inset shows the absorption spectrum of the carbon nanotube film. nature nanotechnology 1

2 supplementary information Supplementary 2: Morphology of carbon nanotube film directly deposited on Si/SiO 2 substrate In addition to the gas-phase filtration method (with membrane filter) employed in the letter, direct deposition onto a substrate is another alternative. Here, as-grown carbon nanotubes were attracted to a Si/SiO 2 substrate under the effect of an applied electrical potential 20. The directly deposited carbon nanotubes tend to exhibit a curled morphology, as shown in Fig. S2. In this case, the effective length of nanotubes in the direction of the current flow of TFTs becomes short. Therefore, the number of internanotube junctions in the current path and the resistance of the network are increased. Figure S2. Morphology of carbon nanotube network directly deposited on Si/SiO 2 substrate by floatingcatalyst CVD. Supplementary 3: SEM image of carbon nanotube network on membrane filter Numerous Y-junctions are observed in the carbon nanotube network collected on the membrane filter before the transfer process, as shown in Fig. S3. Figure S3. SEM image of carbon nanotube network on membrane filter. 2 nature nanotechnology

3 supplementary information Supplementary 4: Evaluation of mobility The carrier mobility ( ) of TFTs is evaluated by, as described in the letter. There are two main methods to estimate the gate capacitance (C) per unit area, one of which is the parallel plate model,, where and t ox is the relative dielectric constant and thickness of the insulator layer, respectively, and 0 is the dielectric constant in vacuum. The parallel plate model is commonly used to evaluate the mobility as an index of TFT performance, and it is adopted in the field of TFTs for Si, organic, and other semiconductor TFTs. This model was used to compare the performance with Si-based TFTs and organic TFTs in Fig. 2 in the letter. In the case of carbon nanotube TFTs, however, the parallel plate model overestimates the gate capacitance when the density of nanotubes is low. Then, a more rigorous model which takes into account the realistic electrostatic coupling between sparse nanotubes and the gate electrode is often used to estimate the gate capacitance of carbon nanotube-based TFTs 2,16. In this model, the gate capacitance is expressed by 2,16 where C Q is the quantum capacitance of carbon nanotubes, 0-1 is the linear density of nanotubes, and is the radius of nanotubes. In this case, the gate capacitance (hence the mobility calculated by equation (S1)) becomes lower (higher) than those given by the parallel plate model. In Fig. 2, we re-evaluated the mobilities with the parallel plate model for those evaluated by the rigorous model in Refs. 3 and 13. If the rigorous model is applied to the present TFTs, the mobility of the device shown in Fig. 1d is evaluated to be 634 cm 2 V -1 s -1. In equation (S3), the average radius R of nanotube branches was 0.75 nm as shown in Fig. S1b, and the linear density was 0.54 tubes/μm, as determined by the statistical measurements from an SEM image. The highest mobility is 1,236 cm 2 V -1 s -1 with an on/off ratio of (S1) (S2) (S3) Supplementary 5: Degradation in on/off ratio with V DS In previous works 3,17,18, it has been reported that the on/off ratio of CNT TFTs is significantly degraded with increasing V DS. In contrast, the degradation in the on/off ratio of the present devices is quite small as shown in Fig. 1d. Here, we discuss the mechanism of the on/off degradation. In Fig. S4, we provide the degradations of on/off ratios for two types of TFTs with different CNT nature nanotechnology 3

4 supplementary information diameters, 1.1 nm (S4a) and 1.6 nm (S4b) on average. The average diameters were estimated by the absorption spectra of thick films of CNTs grown with the same conditions shown in Fig. S4c. In the case of CNTs with an average diameter of 1.1 nm, the on/off ratios of TFTs slightly decreased with increasing V DS, but remained as high as ~ at V DS = 5 V. In contrast, the on/off ratios decreased significantly with increasing V DS from 0.5 to 5 V for TFTs with 1.6-nm CNTs. The variation of I D -V GS characteristics is shown in the insets. In the case of TFTs with 1.6-nm CNTs, the minority electron current in the off-state increases a few orders of magnitude at V DS = 5 V, so that the on/off ratio degrades drastically. The on/off degradation can be attributed to electrons tunneling through the narrow bandgap at the high drain field. The diameter of carbon nanotubes can be controlled in the present FC-CVD technique by adding CO 2 to the source gas S1. Figure S5 shows the absorption spectra of the carbon nanotubes grown with CO 2 of 0, 1, 2, 3, 4 cm 3 /min. Thus, the average diameters were evaluated to be 1.1, 1.2, 1.3, 1.6, and 1.9 nm, respectively. Figure S4. Degradation of on/off ratio with V DS. a. On/off ratios of five TFTs based on carbon nanotubes with an average diameter of 1.1 nm at V DS of 0.5 and 5 V. The inset shows typical I D -V GS characteristics. b. On/off ratios of six TFTs based on carbon nanotubes with an average diameter of 1.6 nm. c. Absorption spectra of carbon nanotube films grown under same conditions as those used in TFTs. From the peaks of S 11 bands, we evaluated the average diameters of nanotubes to be 1.1 and 1.6 nm for TFTs shown in a and b, respectively. 4 nature nanotechnology

5 supplementary information cm 3 /min CO 2 1 cm 3 /min CO 2 2 cm 3 /min CO 2 Absorbance (a.u.) cm 3 /min CO 2 4 cm 3 /min CO nm 1.6 nm 1.3 nm 1.2 nm 1.1 nm Wavelength (nm) Figure S5. Absorption spectra of carbon nanotubes grown under different CO 2 flow rate. Supplementary 6: Concentration of metallic nanotubes The metal/semiconductor ratio was evaluated from the absorption spectrum (Fig. S6) on the basis of the method proposed by Miyata et al. S2 A nonlinear fitting is used to subtract the background absorption. S3 The metallic nanotube concentration (R Metal ) is evaluated by or where I S11, I S22, and I M11 are the integrated intensities of S 11, S 22, and M 11 bands, respectively. The ratio of 30% is almost equal to the theoretical value of 33%, which shows no significant chirality selectivity in the present growth method. (S4) Figure S6. Absorption spectrum of carbon nanotube film. nature nanotechnology 5

6 supplementary information Supplementary 7: Collection time dependence of carbon nanotube density The carbon nanotube density is proportional to the collection time as shown in Fig. S7. Hence, it can be controlled precisely by adjusting the collection time. (g) rate=0.07 m -2 s Density ( m -2 ) Collection time (s) Figure S7. Carbon nanotube networks with different collection times. a f, SEM images of carbon nanotube network collected for 2, 3, 4, 5, 7, and 10 s, respectively. g, Carbon nanotube density dependence of collection time. Supplementary 8: m-value for various CNT Figure S8a to S8c shows the on- and off- current dependence on L ch for collection times of 2, 4, and 10 s, respectively. The m values for on- and off- currents (m on and m off ) are shown as a function of collection time in Fig. S8d and as a function of the effective coverage of the network in Fig. S8e. For a collection time of 10 s, m on and m off are close to unity, where the carbon nanotube network behaves as a classical 2D conductor, i.e. I on ~ L 1 ch. As the collection time decreases, CNT decreases and m on and m off increases. This indicates that the conduction in the film changes from a classical 2D conductor to that of a network-like-conductor described by percolation theory. In addition, m off increases more rapidly than does m on, because off-current flow through only metallic nanotubes and the effective density of nanotubes is lower than that for on-current flow. To obtain a high on/off ratio, the difference between m on and m off should be large, given that I on / Ioff ~ L m ch on m off, i.e., the on/off ratio increases with the exponent m off m on as a function of L ch. For a collection time of 2 s, the large difference between m on (= 1.3) and m off (= 14) leads to the rapid increase in the on/off ratio with the increase in L ch. The m on and m off are plotted as a function of the filtration time in Fig. S8d. The optimized nanotube density in the network, which is controlled by the filtration time, is a key factor for realizing high on/off ratio. In the case of bundled nanotubes, the gate field can be screened by the metallic nanotubes in the bundle. This makes the bundle behave as an electrical metallic wire, and degrades the on/off ratio of TFTs. 6 nature nanotechnology

7 supplementary information In the present carbon nanotube film, even though there exist some bundles, individual nanotubes are dominant, as shown in Fig. S1. In Fig. S8e, we plotted m on and m off as a function of the effective coverage. Here, the effective coverage is CNT L 2 CNT for m on and 0.3 CNT L 2 CNT for m off, assuming the concentration of metallic nanotubes to be approximately 30%. All m-values can be plotted on a curve for the assumption. This implies that the bundling effect on the on/off ratio is negligible in the present sample. Figure S8 a c, On- and off- current versus L ch for collection times of 2, 4, and 10 s, respectively. d, m values for on- and off- currents as a function of collection time. e, m value as a function of effective nanotube coverage. Here, L CNT and the concentration of metallic nanotubes are assumed to be 10 μm and 30%, respectively. Supplementary 9: Hysteresis Hysteresis was observed in the present TFTs. Figure S9a and S9b respectively show the I D -V GS and g m -V GS characteristics of a typical carbon nanotube TFT measured at a sweeping rate of 0.7 V/s for V GS from 5, +5, to 5 V. The maximum transconductances at the linear region (V DS = 0.5 V) are 5.2 and 3.4 S/mm for forward and backward sweeps, respectively. We used the transconductance obtained in the forward sweep to evaluate the mobility in the letter. nature nanotechnology 7

8 supplementary information The hysteresis could adversely affect the repeatable and robust operation of logic circuits. In Fig. S9c, we provide the input-output characteristics of an inverter measured for forward and backward sweeps of input voltage. Under the existence of hysteresis, the noise margin is represented by the area of the smallest eyes formed in the folded transfer curves. In the present inverter, eyes remain apparent in the folded transfer curves, and the operation of logic circuits can be achieved. Figure S9. a, I D -V GS and b, g m -V GS characteristics of typical carbon nanotube TFT showing hysteresis. V GS was swept from 5, +5, to 5 V. c, Input-output characteristics of inverter with hysteresis. The input voltage was swept from 5, 0, to 5 V. 8 nature nanotechnology

9 supplementary information Supplementary 10: Reset-set flip-flops Figure S10 a, Reset-set flip-flop constructed from a pair of cross-coupled NOR logic gates. b, Reset-set flip-flop constructed from a pair of cross-coupled NAND logic gates. Each panel includes an optical micrograph of the device, circuit symbol, truth table, and input-output characteristics. * denotes no change in output, and N/A denotes not applicable. Supplementary 11: Uniformity of carbon nanotube film Figure S11. Sheet resistance and optical transmittance distribution on carbon nanotube film transferred to PET substrate from filter with diameter of 110 mm. nature nanotechnology 9

10 supplementary information Figure S11 shows the spatial distribution of sheet resistance and optical transmittance at 550 nm of a carbon nanotube film transferred onto a PET substrate from a filter of 110 mm in diameter. The deviations are as low as 2.8% and 0.13% for sheet resistance and transmittance, respectively. Reference S1. Tian, Y., Jiang, H., Pfaler, J. V., Zhu, Z., Nasibulin, A. G, Nikitin, T., Aitchison, B., Khriachtchev, L., Brown, D. P. & Kauppinen, E. I. Analysis of the Size Distribution of Single-Walled Carbon Nanotubes Using Optical Absorption Spectroscopy. J. Phys. Chem. Lett. 1, 1143 (2010). S2. Miyata, Y., Yanagi, K., Maniwa, Y. & Kataura, H. Optical evaluation of the metal-to-semiconductor ratio of single-wall carbon nanotubes. J. Phys. Chem. C 112, (2008). S3. Itkis, M. E., Perea, D. E., Jung, R., Niyogi, S. & Haddon, R. C. Comparison of analytical techniques for purity evaluation of single-walled carbon nanotubes. J. Am. Chem. Soc. 127, (2005). 10 nature nanotechnology