The use of carbon nanotubes (CNT) as components in high-frequency electronics has garnered much attention due to their favorable characteristics such as large mobilities, high transconductance, and long mean-free paths. Aside from the popular application of CNTs as high-frequency field-effect transistors,^1-5 other successful applications include their use as RF detectors and mixers. The use of CNTs as an RF mixer has been demonstrated in various arrangements by Appenzeller et al. and later by Rosenblatt et al. up to 50 GHz, as well as by Pesetki et al. who measured frequency independence up to 23 GHz.^6-8 All the preceding work utilized the nonlinearity of the drain current with respect to the gate-source I_D(V_GS) relationship. More recently, Rodriques et al. have demonstrated similar mixer properties of heterodyne microwave detection up to the low gigahertz frequency at T = 77 K but this time by taking advantage of the nonlinearity of the source-drain I_D(V_DS) relationship created by the zero-bias anomaly that manifests at low temperatures.⁹ In this work we utilize room-temperature nonlinearities present in the source-drain I_D(V_DS) relationship and report experimental results for a carbon nanotube based amplitude-modulated (AM) demodulator with modulation frequencies up to 100 kHz. Our device thus represents a room-temperature two-terminal nonlinear device, simpler than prior three-terminal mixers/detectors. Though not optimized, it represents the first such demonstration, similar to that proposed in Manohara et al.¹⁰ Additionally, we present noise measurements of a CNT RF detector. Finally, the CNT based demodulator was successfully demonstrated in an actual AM radio-receiver demodulating high-fidelity music. This represents a simple application of a CNT that can demonstrate the utility of nanotechnology in the wireless field.

Carbon nanotubes were synthesized on high resistivity Si wafers (>8000 cm) to minimize the detrimental effect of parasitic capacitance at high frequencies. Using optical lithography, catalyst regions were patterned onto the wafer and after 1 h of sonication an aqueous solution of 100 mM FeCl₃ catalyst was applied for 10 s and rinsed with DI water. The CVD growth process is identical to that detailed elsewhere.^11,12 Subsequent to the nanotube growth, Pd (20 nm)/Au(80 nm) electrodes were evaporated onto the nanotubes with a gap-spacing of 50 m and a width of 300 m. Only samples with a single CNT bridging the gap were used for this work. To perform high-frequency measurements the sample device was incorporated on a microwave mount with a pair of SMA connectors and microstrip line connecting the device as shown in Figure 1. A total of four devices with semiconducting CNTs were tested, and all were capable of acting as an AM demodulator. The conductance vs gate voltage of the semiconducting CNT under study is presented in Figure 2.

	Figure 1 Schematic of the test-setup for the CNT-based AM demodulator. SEM image of a CNT (right).
	Figure 2 (a) Plot of the source-drain differential conductance vs gate (substrate) voltage of the semiconducting CNT. (b) Current-voltage (IDS vs VDS) curve.

To determine specific features of the nanotube's use as a demodulator, a simple test setup was devised, as shown in Figure 1. An Agilent E4428C signal generator, with amplitude modulation, functioned as the RF source transmitter (TX) and was fed through a MiniCircuits 0.1-6000 MHz bias tee and into the sample device. Sinusoidal modulation frequencies of 0.01-100 kHz were used to amplitude-modulate (AM) the RF carrier with an 80% modulation depth. The CNT along with a sense resistor and a lock-in amplifier (SR-810) functioned as the receiver (RX) in this setup. Extraction of the modulation signal from the RF carrier was performed by the CNT and the lock-in amplifier, which was tuned to the modulation frequency and used to measured the voltage-drop of the signal across the sense resistor.

The CNT is capable of demodulating an amplitude-modulated RF signal due to its nonlinear current-voltage (I_DS vs V_DS) characteristics. It can be shown that such nonlinearities can rectify a portion of the applied RF current, which to first order comes out to be

	Figure 3 (a) Comparison of demodulated current (red crosses) and d2I/dV2 (blue dots) with respect to the bias voltages, VB, showing a very good match. (b) Linear modulation current detected by a lock-in amplifier across a 100 k resistor, indicating that I is proportional to VRF2 (f = 1 GHz, P = 0 dBm, fmod = 13 Hz).
	Figure 4 Demodulated current amplitude as measured with respect to the modulation frequency (f = 1 GHz, Pwr = -5 dBm, R = 100 , and VBB = 2 V).

Maximizing the demodulated signal can be achieved through proper biasing of the CNT. As evident in Figure 3a, one can obtain maximum demodulation by biasing the CNT such that the operating point is centered on the maximum nonlinear portion of the I-V curve. Due to the inherent symmetry of the nanotube, two such operating points exist at ±1 V. The maximum current responsivity was measured to be 125 nA/mW and was found to be independent of back-gate voltage.

Considering that the CNT resistance is on the order of 100 k, from an RF point of view, a large impedance mismatch will exist between the CNT and the 50 characteristic impedance of the transmission line, resulting in a strong microwave signal reflection off the CNT. Because the power available from the source is P_AVS = V_RF²/8Z₀, and the RF voltage at the CNT is V_RF due to Z_CNT Z₀, using eq 1, we obtain I/P_AVS = 2(d²I/dV²)Z₀ for the responsivity of the CNT demodulator. The circuit for this analysis is presented in Figure 5B. This indicates that the resistance of the CNT is independent of the device's responsivity insofar as the second derivative of the CNT is the same. Taking the maximum measured value for second-derivative as 4 A/V², one arrives at a responsivity of 400 nA/mW, which is comparable to the measured value of 125 nA/mW.

	Figure 5 (A) Demodulated signal at various frequencies. Parasitic capacitance shorts the RF signal at frequencies >2 GHz. (B) Schematic of RF equivalent circuit.
	Figure 6 Schematic of CNT radio demonstration.

The effectiveness of the device at detecting the modulation signal up to 100 kHz was found to be limited by extrinsic parameters of the experimental setup and not due to the CNT itself. Due to capacitance within the bias tee and coax cable in conjunction with the sense resistor, an RC low-pass filter was established, thus giving a roll-off in the high audio frequency range of the demodulated signal. To minimize this effect, the detection resistor and the bias-tee's capacitor were reduced to 100 and 100 pF, respectively. The roll-off was measured to have a -3 dB corner at 40 kHz, as shown in Figure 4, which is well above the upper range of human hearing. Signal loss due to the inductor of the bias tee was measured to be -1.5 dB at 100 kHz, which is rather insignificant compared to the other sources of attenuation. As expected, at high carrier frequencies (>2 GHz) the parasitic capacitance resulted in a strong degradation in the received signal (Figure 5A). This is predominantly due to the relatively large contact pads used (300 m × 1000 m).

Noise measurements were performed on the CNT demodulator system operating at a carrier frequency of 1 GHz and bias voltage of 2.5 V. The system voltage-noise density, which includes noise from the lock-in amplifier, sense- resistor, and CNT was measured to be 40 × 10^-9 (V/Hz^1/2) at an audio frequency of 1 kHz. Using the measured responsivity, _I, of 125 nA/mW together with the device resistance of 100 k, the noise-equivalent power (NEP) is calculated using NEP = v_n/(_IR) (W/Hz^1/2) and is 3 nW/Hz^1/2. This puts an upper limit on the noise equivalent power of the CNT itself.

Utilizing the above documented effect, we demonstrate a simple design for a CNT based radio receiver (see Figure 6). Here the carbon nanotube functions in the critical role as the receiver's AM demodulator. The transmitter portion of the demo utilizes a signal generator to create a 1 GHz RF signal that is externally amplitude modulated (AM) with music by an IPod and fed to a dipole antenna for wireless broadcast (see Supporting Information). On the receiver side, the RX antenna picks up the 1 GHz RF signal, feeding it though a bias-tee and onto the carbon nanotubes where it is rectified. The distance between the TX and RX antennas was limited to ~1 m, but that can be improved by simply including a standard front-end preamplifier to boost the received signal before sending it on to the CNT for demodulation. A 1.5 V battery is used to properly bias the CNT for maximum demodulation. A differential pre-amplifier then amplifies the voltage drop across a sense resistor, and the high-fidelity audio is fed to a speaker for audio broadcast. The audio-quality of the signal demodulated by the CNT was very clear and indistinguishable to the human ear from listening to the music directly (see Supporting Information).

To predict how to optimize device performance as a function of length, one would need a quantitative and detailed theory of nanotube I-V curves, and their nonlinearity. Although numerical simulation code exists that can predict nanotube I-V curves, a detailed study of the nonlinearity of CNTs as a function of length has not yet been performed. In the absence of such studies, we may predict on the basis of general physical principles methods to optimize the CNT length to maximize the nonlinearity.

Considering that the nonlinearity in I-V originates from phonon scattering processes, one can further optimize the responsivity of the CNT demodulator by maximizing this nonlinear influence.^14-16 In general, this can be accomplished by decreasing the length of the nanotube to an optimum value. Depending whether one is in the low or high voltage bias regime, the dominant scattering mechanism would be acoustic phonon scattering or optical phonon scattering, respectively. In the limit of each of these regions the slope of the nanotube's I_DS vs V_DS curve can be expressed as G = (4e²/h) × l_i/(l_i + L), where L is the nanotube length and l_i equals l_ap ~ 300 nm for acoustic phonon scattering in the low bias regime and l_op ~ 15 nm for optical phonon scattering in the high bias regime.¹⁶ The nonlinearity manifests as the bias voltage transitions from a region with one dominated scattering mechanism to the other, which in general can be maximized by considering what length nanotube, L, would result in the greatest difference in the slope of I-V between the two regions. For example, if we consider the mean-free-path lengths stated above to be generally accurate, the difference in the slopes is maximized when the nanotube length is ~100 nm. If the nanotube length is decreased further, ballistic transport dominates and the nonlinearity in I-V is again reduced. For long nanotubes (>10 m) other scattering processes would become significant such as defect induced elastic scattering, which further complicates the analysis. Other mechanisms typically responsible for nonlinear I-V characteristics such as a Schottky barrier at the contacts were of negligible contribution due to the use of Pd ohmic contacts.¹⁷ Furthermore, because both metallic and semiconducting CNTs display this behavior, these scaling arguments could be applied to both cases. Thus, although the observed nonlinearity is rather mild, it can be dramatically improved through careful optimization.

We have successfully demonstrated and analyzed the use of a carbon nanotube to demodulate an AM (amplitude modulation) microwave signal in the application of an AM radio receiver. As such, this work represents a step toward a systems demonstration as opposed to a device demonstration, an important step that addresses the field of nanotechnology, as opposed to nanoscience. Though we have only demonstrated the critical component of the entire radio system out of a nanotube (the demodulator), it is conceivable in the future that all components could be nanoscale, thus allowing a truly nanoscale wireless communications system, as we envisioned in ref 18. Thus, this work takes a step toward enabling such an integrated nanosystem.

Acknowledgment

This work was supported by the Army Research Office and the Office of Naval Research.

Note Added after ASAP Publication. Since Web publication of this manuscript the authors have become aware of similar work demonstrating nanotube radio performance at UIUC in the group of Professor John Rogers.¹⁹ Manuscript was originally published ASAP October 17, 2007; the updated version was published October 30, 2007.