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We have developed a wide contact structure for low-noise nanochannel devices based on a carbon nanotube (CNT) network. This low-noise CNT network-based device has a dumbbell-shaped channel, which has wide CNT/electrode contact regions and, in effect, reduces the contact noise. We also performed a systematic analysis of structured CNT networks and established an empirical formula that can explain the noise behavior of arbitrary-shaped CNT network-based devices including the effect of contact regions and CNT alignment. Interestingly, our analysis revealed that the noise amplitude of aligned CNT networks behaves quite differently compared with that of randomly oriented CNT networks. Our results should be an important guideline in designing low-noise nanoscale devices based on a CNT network for various applications such as a highly sensitive low-noise sensor.
Carbon nanotubes (CNTs) have been considered as a promising material for high-performance functional devices such as high-speed field-effect transistors (FETs)1−5 and highly sensitive sensors.6−8 A key parameter determining device performance can be its noise level.(9) Previous works show that CNT-based devices have a rather large 1/f noise compared to conventional semiconducting devices, and the noise amplitude A for the devices based on a bulk CNT network channel was proportional to the resistance R of the CNT-based device like A ~ 10−11 × R.10,11 In the case of rectangular-shaped CNT network channels, the channel width and length were reported to affect the noise behavior.12,13 However, most of previous studies were about CNT network channels much larger than the length of individual CNTs. On the other hand, recent reports showed that CNT networks can be aligned using the nanoscale-wide molecular patterns. Furthermore, the FETs and sensors based on the aligned CNT networks in the nanoscale-wide channels exhibited improved mobility and sensitivity compared with those based on random CNT networks, respectively.14,15 However, increased noise of nanochannel devices can be a major hurdle for its practical applications, and we do not even have a model to describe the noise characteristics of nanoscale channel width devices.
Herein, we developed a wide contact structure for low-noise nanochannel devices based on CNT networks and also report an empirical formula to describe the noise characteristics of structured CNT network channels. This CNT network-based device has a dumbbell-shaped CNT network channel composed of a narrow long channel region and wide CNT/electrode contacts. The wide contact device exhibited relatively small noise compared to a conventional device with rectangular-shaped channels. In addition, we established an empirical formula that can describe the noise behavior of CNT network-based devices, including the effect of contact regions and aligned CNT networks. Interestingly, the systematic noise analysis on our devices shows that the noise characteristics of aligned CNT networks are quite different from that of randomly oriented CNT networks. This result can provide a key strategy to design low-noise high-performance devices based on CNT networks.
The CNT network-based FET arrays were fabricated following the directed assembly strategy as reported before (Supporting Information Figure S1).16−18 In brief, a photoresist (PR) was patterned on the SiO2 substrate, and the PR-patterned substrate was dipped into octadecyltrichlorosilane (OTS) solution (1:500 v/v concentrations in anhydrous hexane) to form nonpolar molecular patterns on the bare SiO2 regions without PR. Then, the substrate was dipped into the SWNT (HiPCo, Carbon Nanotechnologies Inc.) suspensions (0.01 mg/mL in o-dichlorobenzene), subsequently rinsed with o-dichlorobenzene, and dried by nitrogen gas. In the SWNT suspensions, SWNTs were adsorbed onto the bare SiO2 regions and aligned to stay inside the regions. Note that, in case of nanoscale-wide SiO2 regions, the adsorbed SWNTs were rotated to stay in the SiO2 regions, and as a result, they were highly aligned along the channel direction.(16) Last, the metal electrode (Ti/Au) was fabricated by photolithography, thermal evaporation, and lift-off process. We prepared two types of wide contact CNT network-based FETs ((1):1): wide contact devices with a randomly oriented CNT network-based microscale-wide channel or an aligned CNT network-based nanoscale-wide channel. The noise spectra of the fabricated CNT network devices were measured using a Stanford Research Systems model SR 570 current preamplifier and SR 770 FFT network analyzer.
22 shows the AFM topography image of a channel based on a randomly oriented CNT network. The channel width is 2 μm, and the contact width ranges from 2 to 100 μm. As expected, the resistance of device decreased as the contact width increased ((2).2). In our fabrication process, we could reproducibly achieve a uniform monolayer of CNT networks due to the “self-limiting” mechanism where first-adsorbed CNTs blocked the additional adsorption.16,17 In this case, CNT adsorption followed the Langmuir isotherm-like behavior, and the uniformity of the adsorbed CNT monolayer was highly reproducible.14,30 Therefore, we can assume the CNT random network as a uniform film, and the resistance of the device can be written by
where Rch, Rcont, ρch, L, a, rcont, and W represent the channel resistance, contact resistance between metal electrodes and CNT networks, the resistivity of CNT random network, the channel length, the cross-sectional area of the channel, the prefactor of the width-dependent term, and the contact width, respectively. We assumed that the contact resistance is inversely proportional to contact width W with rcont as a prefactor. We fabricated devices with different contact widths (contact width of 100, 20, 5, and 2 μm) and fitted the measured resistance values using 1 to estimate the rcont and ρch (Supporting Information). The rcont and ρch were estimated as 2.58 × 106 and 269 Ω·μm, respectively. It allowed us to estimate the channel and contact resistances of our devices ((22).
Our CNT devices exhibited typical 1/f noise spectrum (inset of of22).(19) The measured noise power spectral density (SI = ΔI2) followed the equation of SI = A(l2/fδ), where the exponent δ is estimated to be ~1. 2 shows the noise amplitude to resistance ratio (A/R) with various contact width W. Previous reports show that A/R ~ constant (~10−11).(10) However, we found A/R ~ W−0.5 for our devices with a structured channel. Specifically, in case of 100 μm width contact, the contact resistance is negligible compared with the channel resistance, and A/R ratio is actually close to 10−11 as reported previously ((22).(10) In the case of narrow contact devices, the contact resistance became a significant portion of the total device resistance, and the A/R ratio increased significantly from the constant value. This result shows that, when the contact resistance is rather large, a significant portion of noise may be originated from the contact between the electrodes and CNT networks.
22 shows the measured noise amplitude values (red dots) of the devices with various contact widths. Each point represents the averaged value of ~10 devices. The green dots represent the values calculated by the previously reported equation A = 10−11 × R and the measured resistance. Note that they matches well only for the 100 μm contact width devices when the contact resistance is relatively small compared with total resistance, while they deviate significantly for rather narrow contact width devices. It indicates that the contact between CNTs and electrodes generates a significant noise, which should be considered for narrow channel devices. We utilized an empirical model to estimate the characteristics of noise originated from contact resistance. Since the contact and channel resistances are connected in series as, the total noise amplitude Atotal can be written as
where ARch and ARcont represent the noise amplitude of CNT network channels and contact parts, respectively.(20) Since previous works show that ARch/Rch ~ constant, we assumed that ARch = α × Rch, where α is a constant. However, since the characteristics of the noise amplitude ARcont are still unknown, we assumed that ARcont = β × Rcontγ, where β and γ are unknown constants. Then, we can rewrite 2 as
We measured the total noise amplitude values of ~40 devices with different contact widths and fitted the data using 3 to estimate the values of α, β, and γ. The fitting results show that
Note that 4 is similar to the previous result, A/R ~ 10−11, of rather large-scale CNT network channels. On the other hand, 5 shows that the characteristics of noise originated from the electrode−CNT contact, which has been ignored in previous works. Note that the noise amplitude ARcont of the contact resistance is not affected much by the contact resistance. Previous work shows that the noise amplitude ARcont (= f·(SRcont/Rcont2)) of perfect Ohmic contact does not depend on the contact resistance.(21) Presumably, the nonzero exponent 0.008 in our case can be attributed to nonperfect Ohmic contact of our devices.22,23 The contact noise was usually ignored in previous works using rather larger scale channel devices. However, it can have a significant effect for the narrow and short channel devices which have a relatively large portion of contact resistance. The black line represents the fitting results based on our 3, 4, and 5, indicating a good fit for the measured data. This result clearly shows that the contact resistance which generates additional random fluctuation should be considered to properly estimate the noise characteristics of small-scale devices.
We also investigated the effect of gate bias voltage Vg on the noise from channels and contacts ((3).3). First, the noise amplitudes of random network devices with 2 and 100 μm contact width were measured under different gate bias voltages ((3).3). The back-gate bias voltage was applied using the underlying p-doped Si substrates. As reported previously, due to the semiconducting CNTs in the CNT network channels, the channel resistance R is a function of gate bias Vg as in R = R(Vg).1−3 Our results show that the positive gate bias Vg resulted in reduced source−drain current Ids and, thus, increased channel resistance R(Vg). It is a typical p-type gating behavior of CNT network junctions under ambient conditions as reported previously ((33).(3) Also note that the noise amplitude A increased as the resistance increased by the positive gate bias voltages. voltages.33 shows the noise amplitude values at different source−drain resistances R(Vg). The devices with 100 and 2 μm contact widths can be fitted by A ~ 10−26.8 × [R(Vg)]3.51 and A ~ 10−27.8 × [R(Vg)]3.44, respectively. Note that both devices exhibited a similar exponent to previously reported values.(19) In the case of 2 μm width devices, a significant portion of the noise came from the metal−CNT contacts, while the noise of 100 μm width devices came mainly from CNT channels. The similar exponent values for both 2 and 100 μm contact widths indicate that the noises from channels and contacts had a similar gate bias dependence. It indicates that the mechanism of noise from the CNT network channels is the same as that from contact. Presumably, the noise source of CNT networks is the contact between individual CNTs, thus exhibiting similar characteristics as the noise from metal−CNT contact.(12)
We performed a similar noise analysis for aligned CNT network channels ((4).4). In this case, the channel width is 100 nm, and the contact width ranges from 100 nm to 10 μm. Note that CNTs in the nanochannel region are aligned along the channel direction, while those in the wide contact region are randomly oriented as mentioned above (Supporting Information Figure S2). More quantitative analysis of CNT alignment in narrow and wide channels can be found in our previous works.14,15 In brief, the degree of CNT alignment in CNT network channels can be measured quantitatively via Raman spectroscopy using the polarized laser light. We observed the larger Raman signals for CNT network channels when more CNTs were aligned along the polarization direction of the laser light. Furthermore, as CNTs were aligned along the channel direction, the conductivity and mobility of the channels were observed to increase continuously without any sharp transition.14,15
In the case of aligned CNT network devices, the devices were turned off at zero gate bias voltage due to the increased probability of semiconducting paths as reported previously.(14) Since we cannot get electric currents large enough for noise analysis at zero gate bias, we turned on the device with −6 V gate bias and performed the electrical characterizations of resistance and noise ((4).4). The resistance Rtotal of the device at −6 V gate bias can be written as
where the subscripts a_ch and r_ch represent the aligned and randomly oriented CNT network channel regions, respectively. R, ρ, L, and a represent the resistance, resistivity, length, and cross-sectional area of the corresponding channel regions marked by subscripts, respectively.
We fabricated devices with different contact widths (10, 4, 2 μm and 100 nm) and fitted the measured resistance values using 6 to estimate the ρa_ch and ρr_ch (Supporting Information). Here, rcont was estimated as 1.37 × 106 Ω·μm from the microscale random network channels with −6 V gate bias, and it was used as a constant during the fitting process. The fitting results show that ρr_ch and ρa_ch are 604.4 and 99.9 Ω·μm, respectively. From these values, we can estimate the resistance of channels and contacts ((44).
44 shows A/R with various contact width. We found A/R ~ W−0.4, where the scaling factor −0.4 was almost the same as that for random CNT network devices ((2).2). In the case of the devices with 10 μm wide contact, the resistance of the contacts and random CNT network regions is negligible, and most of the noise came from aligned CNT networks. Note that the A/R value for those devices with 10 μm wide contact is much larger than that of random CNT networks (~10−11), indicating that the noise from aligned CNT networks is larger than randomly oriented CNT networks with the same resistance values ((44).
44 shows the measured noise amplitude values (red dots) of the devices with various contact widths. The green dots represent the values estimated from the previously reported equation A = 10−11 × R and the measured resistance values. Note that the noise amplitude of aligned network devices deviated significantly from that of random network devices for all contact widths. It indicates that the aligned CNT network-based channels have noise characteristics quite different from random CNT network-based channels.
We utilized the similar empirical model (2 and 3) to estimate the noise characteristics of aligned CNT network channels. Here, the channel part was composed of random and aligned CNT networks. Then total noise amplitude can be rewritten as
where ARa_ch and ARr_ch represent the noise amplitude of aligned and randomly oriented CNT network channels, respectively. We fitted the data in in33 and and44 following the procedure in Supporting Information and found that
These results have several interesting aspects. First, the noise amplitude of the random network channel region has a smaller prefactor compared to 4, presumably due to −6 gate bias voltage in this case. It is a typical noise behavior of p-type CNT networks.(19)9 shows the characteristics of noise originated from the electrode−CNT contact. Note that the exponent of Rcont is larger than that of the randomly oriented CNT channel (5). Since impurities or defect states at the electrode−CNT contact can cause excess noise,22,23 this relatively large exponent can be presumably attributed to the imperfect contact. However, the exponent of Rcont is rather small just like randomly oriented CNT channel devices (5) compared to that of other noise. Significantly, the noise amplitude of the aligned CNT network region ARa_ch follows a power law with quite a large exponent of 4.14 (10), unlike the random CNT network channels which are reported to have the exponent of ~1 (8). Since there are just a few numbers of CNTs in the 100 nm width channel, this nanoscale percolative system is near percolation threshold. Previous works showed that near the percolation threshold, noise amplitude is sensitively changed according to resistance.19,24,25 Thus, the large exponent of our empirical relation (10) is consistent with several previous works.26−29
Using 7, 8, 9, and 10, we can fit the experimental data very well, while the previously reported equation A = 10−11 × R cannot fit the data ((4).4). This indicates that the noise of CNT−electrode contacts and aligned CNT channels has quite different characteristics from that of randomly oriented CNT networks, which should be considered to properly describe the noise characteristics of arbitrary-shaped CNT network-based devices.
We propose a wide contact strategy to fabricate low-noise nanochannel devices based on a CNT network. We fabricated a dumbbell-shaped CNT network channel composed of a narrow long channel region and wide CNT/electrode contacts. We showed that this wide contact structure reduced the amount of noise which comes from CNT/electrode contact region. It indicates that the wide contact nanochannel devices can have the enhanced electrical properties(14) and reduced 1/f noise simultaneously. Interestingly, the systematic noise analysis of our devices revealed that the noise amplitude of aligned CNT network channels depends on its resistance value R, ~R4.14, which is quite different from that of random CNT networks. We provide an empirical formula that can describe the noise characteristics of arbitrary-shaped CNT network-based devices including the effect of contact resistance and CNT alignment. Our work should provide an important guideline in designing low-noise nanochannel devices for various applications such as a highly sensitive low-noise sensor.
Our CNT network-based FET arrays were fabricated following the directed assembly method as reported before (Supporting Information Figure S1).16−18 First, photoresist (PR, AZ5214) was patterned on the SiO2 substrate (oxide 1000 Å, Silicon Materials Inc.) via photolithography, and the PR-patterned substrate was dipped into octadecyltrichlorosilane (OTS, Sigma-Aldrich Inc.) solution for 10 min so that the OTS molecular layer was formed on the bare SiO2 regions without PR. In this case, OTS solution was prepared by dissolving OTS in anhydrous hexane (Sigma-Aldrich Inc.) as 1:500 v/v concentrations. After removing the PR patterns by rinsing the substrate with acetone, the substrate was dipped into the SWNT (HiPCo, Carbon Nanotechnologies Inc.) suspensions for 10 s. In this case, the CNT suspensions were prepared by dispersing SWNTs into o-dichlorobenzene (Junsei Chemical Co., Ltd.) as 0.01 mg/mL concentration. Subsequently, we rinsed the substrate with o-dichlorobenzene and dried it by nitrogen gas. When the substrate was in the SWNT suspensions, SWNTs were selectively adsorbed onto the bare SiO2 regions and aligned to stay inside the regions. It should be noted that, in the case of nanoscale-wide SiO2 regions, the adsorbed SWNTs were rotated to stay in the SiO2 regions. As a result, they were highly aligned along the channel direction. Therefore, we could fabricate the aligned CNT network channel. Last, the metal electrode (30 nm thick Au on 10 nm thick Ti) was fabricated by photolithography, thermal evaporation, and lift-off process.
This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (No. 2010-0000799), the Conversing Research Center Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2010-K001138), System 2010 program of the MKE and Seoul R&DB program (GR070045).
Supplementary fitting methods, additional details on fabrication method, and supplementary figures. This material is available free of charge via the Internet at http://pubs.acs.org.