Large Signal Operation of Small Band-Gap Carbon Nanotube-Based

Aug 2, 2010 - Key Laboratory for the Physics and Chemistry of Nanodevices and College of Chemistry and Molecular Engineering ... Using a top-gate devi...
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Large Signal Operation of Small Band-Gap Carbon Nanotube-Based Ambipolar Transistor: A High-Performance Frequency Doubler Zhenxing Wang,† Li Ding,† Tian Pei,† Zhiyong Zhang,*,† Sheng Wang,† Tao Yu,† Xiaofei Ye,† Fei Peng,‡ Yan Li,‡ and Lian-Mao Peng*,† †

Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics and ‡ Key Laboratory for the Physics and Chemistry of Nanodevices and College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China ABSTRACT A small band-gap carbon nanotube (SBG CNT) with a large diameter of 4 nm has been used to fabricate ambipolar fieldeffect transistors (FETs) with ultrahigh carrier mobility of more than 18 300 and 8300 cm2/V·s for holes and electrons, respectively. Using a top-gate device geometry with 12 nm HfO2 being the gate oxide, the SBG CNT-based FET exhibits an almost perfect symmetric ambipolar transfer characteristic without any noticeable hysteresis, and a highly efficient frequency doubler is constructed based on this near perfect ambipolar FET. The SBG CNT-based frequency doubler is shown to be able to operate in a large signal mode where the input AC signal, being applied to the top-gate electrode, drives the FET operating alternatively in a p- or n-region yielding an output signal at the drain electrode with doubled frequency and high conversion efficiency. For an input AC signal of 1 kHz, detailed frequency power spectrum analysis shows that more than 95% of the output signal is concentrated at the doubled frequency at 2 kHz, with a gain of more than 0.15, and this represents the highest gain so far achieved in carbon-based devices, including graphenebased devices. KEYWORDS Carbon nanotube, field-effect transistor, frequency doubler, radio frequency

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high-performance field-effect transistors (FETs),3,10-14 metallic CNTs can be utilized as interconnecting wires between functional logic units.7,15,16 However, SBG CNTs, which can be either large diameter semiconducting SWCNTs17-19 or double-walled CNTs (DWCNTs) with a semiconducting outer shell and a metallic inner shell,20,21 have not been explored for practical applications. In this letter we show that while with a small current on/off ratio, the SBG CNT of large diameter can be used to fabricate FETs with extremely high carrier mobility and be used most effectively in RF devices, e.g., in building high-performance frequency doublers. SBG CNTs are characterized by their small band gap, low current on/off ratio, and typically ambipolar field-effect characteristics. These CNTs are therefore not suitable for applications in logic circuits as well as interconnects. However, RF applications do not require the device to be in its off state, offering SBG CNTs a promising field of applications. Earlier studies have shown that the ambipolar field-effect characteristics may be used in graphene devices to double the frequency of an AC input without any additional filtering elements.22,23 Here we show that SBG CNTs can not only be used for constructing frequency doublers but also for operating at a large signal mode, i.e., unlike the previously developed small signal RF transistors, which operate only in a small signal region, the SBG CNT-based FET may operate over a much larger signal range. When applied to the gate

arbon nanotube (CNT)-based nanoelectronics has been developed for more than a decade, benefiting from the exceptional electronic properties of CNTs, and many important achievements have been made.1-3 In particular it has been demonstrated experimentally that CNTs generally exhibit extraordinary radio frequency (RF) response up to GHz regime owing to their ultrahigh carrier mobility, suggesting a THz working potential for future CNTbased electronic devices.4-8 For a single-walled carbon nanotube (SWCNT), its electronic properties strongly depend on the ways it is rolled up from a graphene, and this can be fully characterized by its chiral index (n, m), making the carbon-based electronics versatile.1,9 According to the response of the transport behavior of the CNT to an external gate field, CNTs can be broadly divided into three distinct types: (1) typical semiconducting ones with a large band gap and a large current on/off ratio of more than 102; (2) typical metallic ones with a zero band gap and a current on/off ratio of about unity; and (3) those with small band gaps (SBG) and current on/off ratios of between 1 and 100. It is now well established that while semiconducting CNTs are ideal building blocks for high-speed and low-power logic devices, e.g., * Corresponding authors. E-mail: [email protected] (Z.Y.Z.); lmpeng@ pku.edu.cn (L.M.P.). Received for review: 6/15/2010 Published on Web: 08/02/2010 © 2010 American Chemical Society

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FIGURE 1. Device geometry and characteristics of a SBG CNT-based FET. (a) Schematic diagram illustrating the geometry of a CNT-based ambipolar FET and its working principle as a frequency doubler. When a sinusoidal wave is applied to the top-gate electrode of the FET, with the source electrode being grounded, an output sinusoidal wave with doubled frequency is measured at the drain electrode. (b) SEM image showing a top view of a CNT FET. The diameter of the CNT is 4 nm, and the CNT channel length Lg ) 1.2 µm. (c) I-V curve showing the electric breakdown of another long channel device, with Lg ) 2.5 µm and a back-gate voltage VBG ) -20 V. The inset is an AFM image of the CNT, and a height profile along the line, as marked with a white arrow in the figure, showing the diameter of the CNT is about 4 nm. (d) Transfer characteristic of the CNT FET shown in (b) at 4.3 K and with a bias Vgs ) 0.1 V. The insets depict the band diagram for hole (left) and electron (right) injections, respectively.

electrode, the input signal may drive the FET from its p- to n-region yielding a large output in the drain electrode with more than 95% frequency power being concentrated at the doubled frequency of the input AC signal. When compared to graphene FETs, the SBG CNT-based FETs exhibit not only perfect symmetric ambipolar transfer characteristics but also extremely high carrier mobility (in principle larger than 100 000 cm2/(V·s) in CNTs vs about 20 000 cm2/V·s in graphene) on SiO2 substrates due to the suppressed substrate scattering. In addition, the well-behaved saturation behavior of CNT FETs, which is usually not observable in graphene FETs, is also advantageous for achieving a higher cutoff frequency.4 Furthermore the miniaturization of CNT devices can provide more space for future integral circuits design and fabrication. Besides, unlike graphene having a zero band gap, a semiconducting CNT has a well-defined band gap which depends inversely on the diameter of the CNT, thus providing additional means for tunning the current on/off ratio, the transconductance, the frequency response, and the gain of the CNT-based frequency doubler. The device structure and the general working principle of the SBG CNT-based FET are shown in Figure 1a, where the input signal is applied to the top-gate electrode and the output signal is monitored at the drain electrode. A top-view scanning electron microscope (SEM) image of the device is shown in Figure 1b. All devices reported in this work were fabricated on a single CNT which was grown via a catalytic chemical vapor deposition (CVD) method on a heavily © 2010 American Chemical Society

n-doped silicon wafer. The wafer was covered by a 500 nm thick SiO2 which was used here as the back-gate dielectric.24 The source (S) and drain (D) electrodes of the device were defined via electron beam lithography (EBL), and a Ti/Pd metal stack of 20/40 nm was deposited on to the wafer via electron beam evaporation at a base pressure of 10-8 Torr, followed by a lift-off process. The gate stack was also fabricated via EBL, followed by atomic layer deposition (ALD) growth of 12 nm HfO2 thin film at 90 °C as the topgate dielectric. A 5/5 nm Ti/Pd thin film was then evaporated as the gate electrode, followed by a lift-off process to form the final self-aligned FET device structure (see, e.g., Figure 1b) where all the channel region of the device is covered by the top-gate.12 The diameter of the CNT used in this work is about 4 nm, which is measured from the line profile extracted from the atomic force microscope (AFM) image shown in the inset of Figure 1c. An electric breakdown test was carried out on a long channel device with a channel length Lg ) 2.5 µm but without the CNT channel being covered by the top-gate dielectric. The back-gate (the heavily n-doped silicon substrate) of the device was biased at -20 V to electrostatically p-dope the CNT channel and to let the FET be in its on state. It turns out that the breakdown current level of the CNT is about 35 µA (Figure 1c), which is of the same current level as typical CNTs with a moderately large diameter.25 Earlier studies suggest that a CNT of large diameter with electric characteristics similar to Figure 1c and d and with break3649

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FIGURE 2. DC transfer characteristics of CNT FETs. (a) Transfer characteristics for back- (BG, with the top horizontal axis) and top-gate (TG, with the bottom horizontal axis) CNT FETs, respectively. Both the top- and back-gate FET are based on the same CNT channel with a diameter of 4 nm, a channel length Lg ) 1.2 µm, and a bias Vds ) 0.5 V. The dual sweep of the top-gate voltage results in little hysteresis in the transfer characteristics. (b) 3D plot of the top-gate Ids(Vgs, Vds) surface, showing clearly a saturation of the current toward large bias Vds. (c) Top-gate Vds-Vgs transfer characteristics of the CNT FET, with the device being biased by a constant Ids ) 10 µA. The dual sweep of the top-gate voltage results in little hysteresis in the transfer characteristics. (d) 3D plot of the top-gate FET Vds(Vgs, Ids) surface, showing a nearly parabolic-shaped Vds-Vgs relation for current bias Ids ranging from 5 to 15 µA.

down current up to 35 µA could be either a large diameter semiconducting SWCNT or a DWCNT with an outer semiconducting shell and an inner metallic shell.21 The top-gate transfer characteristic of a CNT FET with Lg ) 1.2 µm (Figure 1b) was measured at 4.3 K with a bias Vds ) 0.1 V and shown in Figure 1d. The measurements were carried out in a vacuum chamber with 10-7 Torr base pressure using a Keithley 4200 semiconductor characterization system. The transfer characteristic (Figure 1d) shows a typical ambipolar behavior demonstrating clearly the existence of a small band gap. The band diagrams are also depicted (insets of Figure 1d) for holes (with Vgs < -1 V) and electrons (with Vgs > -0.5 V) to illustrate the operating mechanism of the FET. Since the Fermi level of the S/D contact is aligned to the middle of the band gap of the intrinsic (or unintentionally doped) CNT used here, there exists two small Schottky barriers of almost equal height for both hole and electron injection into the valence and conduction bands of the CNT, respectively.26 In addition, the small Schottky barrier can be significantly thinned and overcome under a relative large bias voltage (100 mV), yielding an almost symmetric ambipolar transfer characteristic even at 4.3 K. Since the device cannot be completely turned off at Vds ) 100 mV, even at 4.3 K, it can be concluded therefore that the band gap of the CNT is much smaller than the bias, i.e., 100 meV. © 2010 American Chemical Society

The DC characteristics of the SBG CNT-based FET were measured at room temperature and shown in Figure 2. Before the growth of the top-gate oxide (12 nm HfO2), the transfer characteristic of the FET with a standard back-gate geometry is asymmetric (Figure 2a), where the current in the p-branch is much larger than that in the n-branch. The tendency for the device to show a stronger p-type branch might be attributed to the effect of oxygen or water in air.27 When a HfO2/metal top-gate stack was fabricated on top of the back-gate FET, the asymmetric transfer characteristic is significantly modified to become almost a perfectly symmetric ambipolar type (Figure 2a).27 The top-gate geometry significantly increased the transconductance of the FET from the original 1 and 0.5 µS for the p- and n-branches (backgate), respectively, to about 13 µS for both p- and n-branches (top-gate), and most significantly [see below, on discussing eq 3] the transfer characteristic may be described very well by a parabolic function over a large input (gate voltage) range on either side of the minimum current point at Vgs ) -1.6 V. The tremendous improvements on the symmetry of the transfer characteristic and the transconductance greatly benefit the performance of the device being used as a frequency doubler.22,23 It is worthy noticing that there exists almost no hysteresis in the top-gate transfer characteristic when performing a dual gate voltage scan, indicating that there exists hardly any movable charges in the top-gate 3650

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dielectric (HfO2). Small or even zero hysteresis in the transfer characteristics enables the use of a constant DC gate voltage during the operation of the device to bias the working point of the CNT FET, and this is of crucial importance for the high performance of the CNT-based frequency doubler. Figure 2a shows that the device current Ids at Vds ) 0.5 V can be modulated from 8 to 16 µA (Figure 2a) by changing the top-gate voltage. While the current on/off ratio (16/8 µA ) 2) is small, we will show below that it is sufficient for the device being used for constructing a frequency doubler. A three-dimensional (3D) plot of the top-gate transfer characteristic surface Ids(Vgs, Vds) is given in Figure 2b, showing that the ambipolar characteristic of the device persists for a rather large bias range (providing a large margin for the operation of frequency doubler), and the device current starts to saturate toward large Vds. The saturation behavior of the current is especially important in achieving the highest cutoff frequency that is possible for a CNT-based FET.4 When the FET is biased at the drain electrode with a constant current source, with Idd ) Ids and the source electrode being grounded, the output Vds can then be directly modulated by the input, i.e., Vgs. Since the source drain resistance Rds is a function of Vgs, i.e., Rds ) f(Vgs), the output drain voltage then becomes

Vds ) Ids · Rds ) Idd · f(Vgs)

FIGURE 3. Schematic diagram illustrating the basic working principle and measurement setup for a CNT-based frequency doubler. The input Vgs is a sinusoidal wave, with a peak-to-peak voltage value of Vpp and a frequency of ω/2π, and is biased at the gate of the CNT FET with Vg,DC. The frequency of the output Vds is doubled, due to an ideal parabolic-shaped DC Vds-Vgs curve. The drain electrode of the FET is biased by a current Idd such that the drain current Ids ) Idd. The resulting output waveform at the drain electrode is monitored by an oscilloscope (OS). The marks A-E represent the corresponding points of the input and output at the same time points.

circular frequency of the input sinusoidal wave. The drain of the CNT FET is biased by a constant current, i.e., Ids ) Idd and also connected to a digital oscilloscope (OS in Figure 3) in order to monitor the output waveform. When the input is at time point A, the FET is at its maximum resistance point, resulting in a maximum voltage at point A in output. After time A, the input drives the FET into its n-region, and FET reaches the minimum resistance point in the Vds-Vgs curve at time point B and hence the minimum point B in the output at the drain. After time B, the input moves back to the central point C, and the output reaches its maximum point C. Beyond time C, the FET begins to work at its p-region and then reaches the minimum point D in output. Finally the input moves back to the central point E again, resulting in an output at point E. The output apparently runs for two periods for a single period of the input, thus frequency doubling is realized mainly due to the perfectly symmetric DC Vds-Vgs characteristic of the FET (as shown in Figure 2c and d). It is obvious that the input signal sweeps from n- to p-branch over a rather large signal range, and it is for this reason we say that the CNT-based frequency doubler works in a large signal mode. All AC measurements reported in this work were carried out in vacuum. The measurement facilities include an Agilent 33220A signal generator, an Agilent DSO7054A digital oscilloscope, and an Agilent N9020A spectrum analyzer. The drain electrode is biased with a current source with Idd ) 10 µA, and the input AC signal is superimposed on a DC voltage Vg,DC ) -1.7 V to optimize the performance of the device (see, e.g., the transfer characteristic shown in Figure 2c). For a 1 kHz input

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Like the transfer characteristics shown in Figure 2a, the Vds-Vgs characteristics are also ambipolar in nature for the SBG CNT device, as shown in Figure 2c and d. A particularly important device feature for the high performance of the frequency doubler is the stability of its working point. Figure 2c shows that the dual sweep of Vgs (with Ids ) 10 µA) between -3 to 0 V introduces hardly any visible hysteresis in the Vds-Vgs curve, making it possible to construct a frequency doubler based on the CNT FET. The 3D plot of the Vds(Vgs, Ids) surface further shows that the FET can work well over a wide range of Ids, from 5 to 15 µA, yielding a variation in Vds of more than 2. The frequency doubler we are going to discuss below is based on this kind of transfer characteristic, and this configuration avoids the use of a series resistance as in the voltage bias measurement for graphene devices.22,23 The working principle of the CNT FET-based frequency doubler and corresponding test setup are depicted in Figure 3. The input signal is the voltage applied on the gate electrode:

Vin ) Vgs ) Vg,DC + 1/2Vpp,insin ωt,

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where Vg,DC is a DC voltage to bias the working point of the FET, Vpp,in is the peak-to-peak amplitude, and ω ) 2πf is the © 2010 American Chemical Society

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FIGURE 4. AC performance of a CNT-based frequency doubler. Input and output waveform for (a) an input 1 kHz sinusoidal wave with input Vpp ) 800 and output Vpp ) 120 mV; and (b) an input 100 kHz sinusoidal wave with input Vpp ) 800 and output Vpp ) 10 mV. (c) Schematic diagram depicts the measurement setup for frequency spectrum analysis. The input signal is applied on the gate of the CNT FET, and the output AC signal is coupled through a bias-T to the spectrum analyzer (SA). (d) Measured output signal spectrum for 1 kHz input (Figure 4a). The four arrows indicate the frequencies of 1, 2, 3, and 4 kHz, respectively, from left to right.

signal, the output resembles excellently well a sinusoidal wave but with a doubled frequency of 2 kHz, as monitored by the oscilloscope (Figure 4a). The input 800 mV peakto-peak voltage value in Vgs covers a large nonlinear range from n- to p-branches (Figure 2c) and results in an output peak-to-peak voltage value of 120 mV in Vds, demonstrating a voltage gain of about 120/800 mV ) 0.15. This value presents the largest gain value so far achieved by a carbon-based ambipolar frequency doubler.22,23 The gain can also be estimated from the DC transfer characteristic (Figure 2c). The Vpp,in leads to a swing in the input ∆Vin ) 800 mV (see the green arrow in Figure 2c), which in turn results in a swing of Vgs or an output ∆Vout ) 160 mV (see the purple arrow in Figure 2c). The gain estimated from the DC characteristic of Figure 2c is therefore 160/800 mV ) 0.2, and this estimated value is basically the same as the measured value of 0.15. For 100 kHz input sinusoidal wave (Figure 4b), the output still resembles a periodic wave with basically a doubled frequency of 200 kHz. However, the waveform is distorted, and the signal is significantly decayed, reducing the gain value to about 1/80 (with Vpp,in ) 800 and Vpp,out ) 10 mV). The signal damping of the whole circuit is largely determined by the total output resistance mainly originated from the current source, which is typically much larger than 1 MΩ, and by the substrate coupling capacitance C, which increases © 2010 American Chemical Society

rapidly with increasing frequency. Nevertheless this situation can be largely improved by replacing the conducting substrate with an insulating one, e.g., quartz, on which CNTs can readily grow. Here, the device performance at high frequency is mainly limited by the parasitic effect due to the external wired configuration and the measurement setup, rather than by the device itself. We have fabricated three FETs on the same SBG CNT, and all of these three FETs exhibit good ambipolar DC characteristics and result in frequency doubling above 100 kHz. This high yield in fabricating doubler devices is largely due to use of the self-align process we developed earlier,12,13 which is known to be able to produce stable and uniform CNT FETs with a yield of more than 80%. To quantitatively analyze the frequency power distribution of the output signal, we introduced a spectrum analyzer in the measurement circuit, as shown in Figure 4c. The output port of the FET (i.e., drain electrode) is connected to a bias-T (which consists of a capacitor and an inductor), with the output AC signal being coupled via the capacitor to the spectrum analyzer (SA in Figure 4c) and the DC current bias Idd being coupled to the drain electrode via the inductor. In this way, the DC current is capacitively decoupled from the spectrum analyzer. The power spectrum of the output signal for 1 kHz input is shown in Figure 4d. The background of the output power spectrum is seen to decrease with increas3652

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ing frequency, as expected for the 1/f noise, and the noise is especially important in the kHz frequency range. Superimposed on the background are three peaks as marked in Figure 4d, locating at 2, 3, and 4 kHz respectively, while the power at the fundamental frequency 1 kHz is hardly distinguishable from the background noise. Almost all output power is concentrated in the 2 kHz peak, i.e., the doubling frequency peak, but there also appears two visible peaks at 3 and 4 kHz which correspond, respectively, to the triple and quadruple frequency. It should be noted that in the output power spectrum (Figure 4d), the peaks at the triple and quadruple frequencies are, respectively, about 20 and 17 dBm lower than that at the double frequency, showing that the peaks at the triple and quadruple frequencies are only about, respectively, 1/100 and 1/50 of the peak at the double frequency. It may be readily estimated from the power spectrum that more than 95% output power of the CNTbased frequency doubler has been converted to that at the double frequency, and this is because the nearly ideal Vgs-Vds characteristic exhibited by the device, as shown in Figure 2c. Assuming a parabolic relation between the output (Vout ) Vds) and input (Vin ) Vgs), i.e.

Vout ) A + B(Vin - Vg,DC)2

FIGURE 5. Transfer characteristics for (a) a short channel (L ) 1.2 µm) top-gate CNT FET (left scale) and a corresponding transconductance curve (right scale) with Vds ) 1 V; and (b) a long channel (L ) 42 µm) back-gate CNT FET (left scale) and a corresponding fieldeffect mobility curve (right scale) with Vds ) 1 V. Both short and long channel FETs were fabricated on a single large diameter CNT with d ) 4 nm.

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with A and B being two constant coefficients. For a sinusoidal input wave at the input port Vin ) Vg,DC + 1/2 Vpp,in sin ωt, simple analysis shows that the output then yields a perfect sinusoidal wave but with doubled frequency

[

Vout ) A +

]

2 2 BVpp,in BVpp,in cos 2ωt 8 8

capacitance Cox ) 2πε0εr/ln (2 + 4t/d) and the quantum capacitance CQ ) 4 pF/cm.5 For the ALD grown HfO2, the dielectric constant εr ) 18, and the film thickness t ) 12 nm. For the CNT used in this work, the diameter of the nanotube d ) 4 nm, and Cox ) 3.8 pF/cm. The total gate capacitance may then be calculated to be 0.24 fF, yielding an intrinsic cutoff frequency fT ) gm/2πCtotal ) 9 GHz for a CNT FET with Lg ) 1.2 µm.4,5 The scaling theory for a short channel CNT FET predicts a 1/Lg2 dependence of the cutoff frequency on the channel length.4 For a FET with Lg ) 100 nm, a cutoff frequency of up to 1.2 THz is then expected. In principle, the operation frequency of our CNT frequency doubler may be significantly increased by optimizing the device structure, wired configuration, and measurement system.28 One of the most important advantages for the CNT being an electronic material is its high carrier mobility, and this is particularly so for a large diameter CNT and is important for RF applications. This is because the carrier mobility scales as d2, and ultrahigh mobility is expected for large diameter CNTs, such as the one used in this work. To further assess the RF potential of the SBG CNT, we extracted the field-effect mobility µFE from another FET which was fabricated on the same CNT as the one used to construct the frequency doubler (Figure 2) but with a

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It may be concluded from eqs 3 and 4 that a perfect parabolic transfer characteristic (Vgs-Vds) will lead to a perfect frequency doubling. The appearance of the peaks at triple and quadruple frequencies in Figure 4d may therefore be attributed to the deviation of the experimental Vgs-Vds characteristic (Figure 2c) from that of a perfect parabolic form (eq 3). Measurement carried out at a higher input frequency up to 100 kHz showed similar high spectral purity at double frequency. The ultimate performance of the CNT-based frequency doubler is largely determined by the intrinsic cutoff frequency (fT) of the CNT FET. To a good approximation, the intrinsic cutoff frequency may be estimated using the relation fT ) gm/2πCtotal, where gm is the peak transconductance, and Ctotal is the total gate capacitance of the CNT FET. From the transfer characteristic, as shown in Figure 5a, a peak transconductance of gm ) 14 µS is obtained. The total gate capacitance Ctotal can be considered as a series capacitance of Cox and CQ, with the dielectric oxide © 2010 American Chemical Society

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much longer channel length to validate the use of the diffusive transport theory and to minimize the effect of the contact resistance on the estimated µFE. Within the diffusive transport regime, the field-effect mobility µFE may be extracted from the transfer characteristic of the back-gate FET,

µFE )

Lg 1 dIds CBG Vds dVgs

that achieved in corresponding graphene devices, signifying the potential applications of the SBG CNTs in radio frequency devices. Acknowledgment. This work was supported by the Ministry of Science and Technology of China (Grant nos. 2006CB932401 and 2006CB932402), the Fundamental Research Funds for the Central Universities, and National Science Foundation of China (Grant no. 60971003).

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REFERENCES AND NOTES (1)

where the channel length Lg ) 42 µm, and the back-gate capacitance CBG ) 0.22 pF/cm (for a 500 nm SiO2, 4 nm CNT diameter, an average dielectric constant of 2.5 for SiO2/air,29 and negligible quantum capacitance). The resulted mobility characteristic is shown in Figure 5b along with corresponding transfer characteristic. The peak mobility for holes and electrons is found to be 18 300 and 8300 cm2/V·s, respectively. Although the ambipolar characteristic of Figure 5b is not very symmetric for the backgate device geometry, it can be largely improved by utilizing the top-gate geometry, as for a short channel device (Figure 2a). The high mobility of the SBG CNT is mainly due to the large diameter of the nanotube and the lack of effective surface scattering for the special cylinder structure of the CNT.30 It should be noted that the carrier mobility value does not depend strongly on whether the nanotube is a SWCNT or a multiwalled CNT. This is because the transport properties of a CNT FET are determined mainly by the outermost shell, i.e., the main conducting channel, and are hardly affected by the inner shells under low bias.31 It should be noted that the mobility value achieved here for a SBG CNT-based FET on SiO2 substrate is much higher than that of corresponding graphene devices,32-34 and this may potentially lead to an outstanding performance of the CNT-based frequency doubler.4,5 In conclusion, a SBG CNT with a large diameter of 4 nm has been utilized for fabricating FETs and shown to exhibit an ultrahigh carrier mobility of more than 18 300 for holes and 8300 cm2/V·s for electrons in the back-gate device geometry and an asymmetric transfer characteristic with a small current on/off ratio of about 2. The asymmetric transfer characteristic has been shown to be significantly modified to become almost symmetric in the top-gate geometry using a thin layer of 12 nm HfO2 as the top-gate dielectric. This ambipolar transfer characteristic is found to excellently follow a parabolic Vds-Vgs relationship, and when biased with a constant current in the drain electrode, it yields an almost perfect frequency doubling to the input AC signal via the top-gate of the CNT FET. Detailed frequency power spectrum analysis shows that for 1 kHz input signal, more than 95% output signal is concentrated at the doubled frequency of the input fundamental signal, and a signal gain of up to 0.15 is achieved. This gain value is much larger than © 2010 American Chemical Society

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DOI: 10.1021/nl102111j | Nano Lett. 2010, 10, 3648-–3655