A carbon nanotube optical rectenna

An optical rectenna—a device that directly converts free-propagating electromagnetic waves at optical frequencies to direct current—was first proposed over 40 years ago1, yet this concept has not been demonstrated experimentally due to fabrication challenges at the nanoscale2,3. Realizing an optical rectenna requires that an antenna be coupled to a diode that operates on the order of 1 pHz (switching speed on the order of 1 fs). Diodes operating at these frequencies are feasible if their capacitance is on the order of a few attofarads3,4, but they remain extremely difficult to fabricate and to reliably couple to a nanoscale antenna2. Here we demonstrate an optical rectenna by engineering metal–insulator–metal tunnel diodes, with a junction capacitance of ∼2 aF, at the tip of vertically aligned multiwalled carbon nanotubes (∼10 nm in diameter), which act as the antenna5,6. Upon irradiation with visible and infrared light, we measure a d.c. open-circuit voltage and a short-circuit current that appear to be due to a rectification process (we account for a very small but quantifiable contribution from thermal effects). In contrast to recent reports of photodetection based on hot electron decay in a plasmonic nanoscale antenna7,8, a coherent optical antenna field appears to be rectified directly in our devices, consistent with rectenna theory4,9,10. Finally, power rectification is observed under simulated solar illumination, and there is no detectable change in diode performance after numerous current–voltage scans between 5 and 77 °C, indicating a potential for robust operation. A single-frequency energy conversion efficiency greater than 90% has been demonstrated11 for a rectenna operating at much lower frequencies in the microwave spectrum (∼2 GHz). Theory suggests9,10 that efficiencies this high could also be achieved for an optical rectenna using an ideal diode—that is, one with ultralow capacitance and resistance, and high nonlinearity and asymmetry. The cutoff frequency for a rectenna is defined4 as fc = 1/(2πRACD) when the diode resistance is much greater than the antenna resistance, where RA is the antenna resistance and CD is the capacitance of the rectenna diode. This assumption is probably appropriate for nanoscale rectenna because, although a number of efficient designs for optical antennas exist12, contact and quantum resistances are typically large in nanoscale devices13. Because the diode capacitance is given by CD = ε0εA/d (ref. 4), where ε0 is the permittivity of vacuum, ε is the relative permittivity of the insulator, A is the area and d the insulator thickness, reducing the diode area is a simple approach to increase the cutoff frequency and produce an optical rectenna. A natural approach for efficient antenna–diode coupling is to use one electrode in a metal–insulator–metal (M-I-M) diode2,3 as the antenna. Carbon nanotubes can be used to absorb electromagnetic radiation in essentially the entire electromagnetic spectrum by both free carrier (intraband) and excitonic (interband) absorption processes14–16, which, when combined with high carrier mobilities, makes them especially suited for broadband photonic and optoelectronic applications17,18. In contrast to single-walled carbon nanotubes, which can be semiconducting or metallic based on their chirality, multiwalled carbon nanotubes (MWNTs) exhibit metallic properties19 due to the presence of at least one metallic chirality and do not typically show an excitonic photovoltaic effect15. The photoresponse of metallic nanotubes is usually caused by thermal effects15. However, the ability of metallic nanotubes to behave as antennas5,6, coupled with their small tip area, make these materials ideal candidates for the fabrication of a combined antenna–rectifying diode (a rectenna, Fig. 1a). Vertically aligned arrays of MWNTs were grown by chemical vapour deposition, and MWNT-I-M tunnel diodes were fabricated at the nanotube tips using atomic layer deposition (ALD) of Al2O3 (Fig. 1b,c) and thermal evaporation of a semi-transparent lowworkfunction top metal electrode (Fig. 1b; see Methods). Our device structure (MWNT-Al2O3-Ca) is analogous to numerous metal whisker point contact diodes4,20 connected in parallel, because the MWNTs are vertically aligned, physically isolated from each other by the conformal Al2O3 coating (Fig. 1b,c), and connected to an approximately planar top metal contact film (Fig. 1b). An insulator typically needs to be less than ∼2 nm thick to allow significant electron tunnelling and rectification21, but the intrinsic electric field (the field due to asymmetric metal workfunctions) is enhanced (Fig. 2a) at the MWNT tips in our device geometry, similar to the field enhancement that occurs in nanotube field emitters22, which produces an estimated effective insulating barrier thickness of 1.5 nm for a deposited Al2O3 thickness of 8 nm (Supplementary Figs 1–4). We note that the actual atomic interfaces may be separated by a distance smaller than 8 nm due to diffusion of top metal atoms into the oxide during deposition (Supplementary Fig. 4 shows an effective insulating barrier thickness of 2.8 nm for a deposited Al2O3 thickness of 8 nm in a planar device with similar contrast in workfunction). The rectification asymmetry is also enhanced (Supplementary Fig. 5) and the turn-on voltage decreased (Fig. 2b and Supplementary Fig. 1) by the large difference in workfunction between the MWNTs (Supplementary Fig. 6) and Ca. The MWNT-Al2O3-Ca diode has a workfunction difference of 2.1 eV, whereas the diode with an Al top metal has a workfunction difference of only 0.7 eV. Note that devices with the Al top metal contact did not produce a detectable photoresponse in our testing due to their high turn-on voltages. Given that electron transport is most efficient in the axial direction of MWNTs19,23, the diode area where electron tunnelling occurs is probably defined by the outer MWNT tip diameter of 8–10 nm, as illustrated in Fig. 1a. Thus, the diode capacitance is inherently on the order of a few attofarads in our design, which enables operation at petahertz frequencies. To confirm this, specific capacitances on the order of 3 ± 0.6 μF cm for entire devices, or ∼2 aF per MWNT junction, are extracted from capacitance measurements in a standard low-frequency range (Fig. 2c) by using the number density of MWNTs (∼10 cm) to determine the real or active


Turn-on voltage, field enhancement, effective barrier thickness, and asymmetry
Two different metal electrodes with different work functions were tested to correlate the effect of metal work function on rectification ratio and turn-on voltage. Several multiwall carbon nanotube-insulator-metal (MWNT-I-M) devices were fabricated in the same batch to produce similar array heights. These arrays were then coated with 8 nm of Al 2 O 3 in the same atomic layer deposition (ALD) run. The turn-on voltage of MWNT-I-M devices with Ca (work function ~ 2.9 eV) and Al (work function ~ 4.3 eV) top metal electrodes was determined based on the experimental current-voltage curves. The turn-on voltage was defined as the voltage at which a line fit to a linear portion of the current-voltage curve intercepts the y-axis (that is, zero current, which is chosen to be 1 µA). This choice in definition of the turn-on voltage is arbitrary, so the main purpose of this analysis to create a self-consistent picture in which to compare the effects of work function on the onset of significant nonlinearity in our devices, and to estimate the extent of insulator barrier thinning due to geometric field enhancement. Supplementary Fig. 1 shows that the estimated turn-on voltage is 1.3 V smaller for Ca (0.3 V) top contact compared to Al (1.6 V). To determine the effects of geometric field enhancement at MWNT tips on diode rectification and turn-on voltage, we tested planar Au-Al 2 O 3 -Ca diodes, which were fabricated to closely match the contrast in work function and oxide thickness in the MWNT-I-Ca devices for comparison. Planar M-I-M device geometries with glass/Ti/Au-Al 2 O 3 -Ca/Al were fabricated with various areas ranging from 0.01-0.04 cm 2 by first depositing Ti (30 nm)/Au (100 nm) on ultra-smooth glass substrates using e-beam evaporation. Then 8 nm of Al 2 O 3 dielectric was deposited using ALD. Current-voltage characteristics measured on the planar devices with different active areas are shown in Supplementary Fig. 2. The planar devices produced rectification ratios (~ 1.2 at ± 2.75 V d.c. bias) and tunnel currents (~ 1.5 µA/cm 2 at 2.75 V) that are several orders of magnitude lower than the currents produced in the MWNT-I-Ca diodes (Fig. 2b). These results suggests that reduced effective barrier resistance due to geometric field enhancement could contribute significantly to the much higher tunnel currents and asymmetry achieved in the MWNT-I-M diodes. A simple energy level diagram is shown in Fig. 2a to illustrate the potential effects of work function contrast and field enhancement on the resistance to electron tunneling in MWNT-I-M devices. Since the field enhancement is only expected in the forward direction, it contributes to unidirectional thinning of the tunneling barrier. This is because a single diode can be viewed roughly as a MWNT point contact emitter against a planar surface (Fig. 1a). The electron tunneling equations from Simmons 1 are often used to fit experimental data for M-I-M diodes, however it has been shown that while these equations predict the behavior of planar structures qualitatively, the current density is often under-predicted significantly. 2,3 The current-voltage curves of carbon nanotube devices often differs somewhat from the exponential relationship between current and voltage in previous studies, 4 which is consistent with the observation in the MWNT device data in this work. Understanding the limitations of this theory, the Simmons equations were used with the experimentally estimated turn-on voltages to determine the effective barrier thickness of an equivalent planar structure that would produce a current at these voltages. More recent work has developed numerical solutions to electron tunneling through insulators, 5-7 however the original analytical expressions using the WKB approximation are sufficient to examine the qualitative current-voltage behavior of planar devices. 8 The equivalent planar structures were used because carbon nanotube diode data does not fit well to classic tunneling theory because of effects including variation of curvature and electron density of states at carbon nanotube tips. 9,10 The equation for the current density under a forward applied bias for dissimilar electrodes separated by a dielectric barrier is given by Simmons: 11 (1) where, , ϕ is the average potential barrier height with respect to electrode Fermi level, is the applied voltage, Δs is the barrier thickness, m is electron mass, h is Plank's constant, and e is the electronic charge. 11 When the image force potential is considered the effective work function is given as: It should be noted that the expression for λ used here is a factor of 2 smaller than the original Simmons equation, which was in error as noted by Miskovsky et al. 7 For intermediate voltages (eV > φ 1 ) s 2 is: and for high voltages (eV > φ 1 ): (6) ε is the dielectric constant of the insulator, and its value is taken to be 5.1 as determined from the measured capacitance values for 8 nm thin ALD deposited Al 2 O 3 barrier on planar surface (see section 3 below). s is the barrier thickness and Δs = s 2 -s 1 and Δφ = φ 2 -φ 1 . The barrier height at the metallic electrode is the difference between the electrode work function and the electron affinity of the oxide barrier. The barrier height, φ 1 = 1.9 eV for Ca, φ 1 = 3.3 eV for Al, and φ 2 = 4.1 eV for MWNT was taken in the above expressions. All parameters in the current density equation were held constant except for the barrier thickness. A threshold current of 1 µA was set and the effective barrier thickness that would produce the threshold current was calculated. The area used for the current calculation was the projected device area (0.01 cm 2 ) multiplied by the fill fraction of the MWNTs (0.005) for an effective area of 5 ×10 -5 cm 2 . Because the two devices were identical except for the work function of the metal electrode, it was expected that the difference between the work function of Ca and Al could account for the difference in turn-on voltages that was observed experimentally. Since the deposited barrier thickness was the same in both devices, it is expected that the modeled effective barrier thickness of each device would also be the same. The physical barrier thickness of the device is 8 nm, but this does not account for the electron tunneling enhancement produced by the concentrated electric field at the tips of the MWNTs. The effective electron tunneling barrier thickness (s eff ) was determined to be approximately 1.5 nm for both Ca and Al. These are the barrier thickness in a planar device that would produce 1 µA of current at the respective turn-on voltages. A plot of the theoretical current-voltage for Ca and Al planar devices with the aforementioned barrier thickness are shown in Supplementary Fig. 3. This result provided confirmation that the difference in work function of the two top metals was responsible for the change in turn-on voltage between the two device types.
Supplementary Fig. 3. Theoretical current-voltage characteristics and estimated effective barrier thicknesses (s eff ) based on an equivalent planar MWNT-I-Ca and MWNT-I-Al structures (that is, the same material properties were used) that would produce a magnitude of current similar to experimentally observed currents at the turn-on voltages (0.3 and 1.6 V for Ca and Al, respectively). The arbitrary current threshold that defines voltage turn on is 1 µA.
The current-voltage curves for the planar devices (Au-Al 2 O 3 -Ca) were fitted using the above Simmons' theoretical electron tunneling equations by fitting for the effective barrier thickness, s eff . This application of Simmons' equations is also similar to previous work that changed the barrier thickness to fit the model. 8 The data and best-fit theoretical curves are shown in Supplementary Fig. 4 with the experimentally measured data. It can be seen that the theoretical fittings agree well with the measured current-voltage curves for three different devices. The s eff in the planar Au-Al 2 O 3 -Ca diodes is estimated to be 2.8 nm from fitting Simmons' theory to three devices with different areas (0.01 cm 2 , 0.03 cm 2 , 0.04 cm 2 ) as shown in Supplementary Fig. 4. The Au and Al 2 O 3 layers were measured with atomic force microscopy to be atomically smooth (rms roughness of 0.52 ± 0.06 and 0.64 ± 0.02 nm, respectively); therefore, it is unlikely that surface roughness contributes to field enhancement in the planar diodes, as has been observed in prior work. 8 The fact that the effective barrier thickness is thinner than the physical barrier thickness means that the tunneling equations under predict the current density, which is consistent with previous findings. 8,12 The nearly twofold reduction in s eff for MWNT-I-M diodes compared to the equivalent planar structures presents strong evidence that field enhancement at MWNT tips contributes to effective barrier thinning in these devices. However, the effective device field enhancement is expected to be less than that of a single carbon nanotube because of collective screening of the external field by neighboring tubes in the array. 13

Effect of MWNT work function on electrical performance
Different carbon nanotube growth conditions or substrates can produce MWNT structures with different morphology and can result in different electrical properties and work functions. 14 The work functions of MWNTs grown on Si substrates with different resistivities were measured by Kelvin probe on three different spots on the same sample and on MWNTs grown in different batches ( Supplementary Fig. 6a). The MWNTs that were grown on medium resistivity Si substrates (0.01-0.05 Ω.cm) exhibited a higher work function (5 eV) than the work function of MWNTs that were grown on low resistivity Si (0.001-0.005 Ω.cm), which was 4.8 eV. The MWNTs with 5 eV work function were used in the devices in the main text.
In order to correlate the diode current rectification with the bottom MWNT electrode work function, Al 2 O 3 was deposited on the two MWNT samples followed by the deposition of a Ca top metal electrode. The inset in Supplementary Fig. 6a indicates clearly that the rectification in the current for a given applied d.c. bias is higher in devices that use MWNTs with a higher work function. These results were reproducible on several devices as shown in Supplementary  Fig. 6. Evaluation of the samples in scanning electron microscope (SEM) revealed that the MWNTs that were grown on low resistivity substrates were less straight in comparison to the MWNTs that were grown on medium resistivity substrates ( Supplementary Figs. 6b and 6c). The higher degree of carbon nanotube waviness could explain the lower work functions measured on the MWNTs grown on low resistivity Si substrates because such waviness could increase defects, entanglement, and as a result cause a substantial decrease in the electrical conductivity of the MWNTs. 15

Capacitance measurements of MWNT-O-M diode arrays
The measured capacitances ( ) based on the apparent device area (0.1 cm 2 ) of MWNT-I-M diode arrays with different oxide thicknesses (Fig. 2c) were nearly constant in a standard low frequency range (up to 10 6 Hz). The results do not show the inverse thickness relation of a conventional parallel plate capacitor because the permittivity of nanoscale oxide insulators can decrease with thickness. 16 For the MWNT-O-M arrays fabricated with 8 nm Al 2 O 3 , specific capacitance of approximately 3.4 µF/cm 2 or roughly 2 attofarads per MWNT junction, and a dielectric constant (ε) of 3.8 can be extracted using the following expression The measured capacitance is 1.7 nF for an 8 nm oxide (Fig. 2c). The measured MWNT diameter is approximately 8 nm, so the area of a MWNT tip = π x 4 2 x 10 -14 cm 2 = 50.24 x 10 -14 cm 2 . Based on the number density of MWNTs estimated from SEM images, there are approximately 10 9 MWNTs in an area of 0.1 cm 2 . Therefore, the actual area A = 50.24 x 10 -14 cm 2 x 10 9 = 50.24 x 10 -5 cm 2 . Hence, the specific capacitance C/A = 1.75 nF/50.24 x 10 -5 cm 2 = 0.0338 x 10 -4 F/cm 2 = 3.38 x 10 -6 F/cm 2 = 3.38 µF/cm 2 . The dielectric constant (ε) of 3.8 can be extracted from the calculated specific capacitance for 8 nm oxide by using the equation, Similarly, the capacitance per junction can be evaluated by dividing the measured capacitance (1.7 nF) by the number of MWNTs in an area of 0.1 cm 2 (10 9 MWNT). Hence, the capacitance per junction is 1.7 nF/10 9 , which is 1.7 x 10 -18 F.
The measured capacitances (at 1 kHz and 20 mV rms ) of the planar Au-Al 2 O 3 -Ca devices with 8 nm of oxide as a function of area (ranging from 0.01-0.04 cm 2 ) are shown in Supplementary Fig. 7. The capacitance per unit area (C/A) as extracted from the linear fit of the slope of capacitance versus area curve is 569 nF/cm 2 . Using the value of C/A in a conventional parallel plate capacitor model where capacitance is given by equation (8), a dielectric constant ( ) of 5.14 is calculated for the ALD deposited 8 nm Al 2 O 3 . related to the rectified d.c. current as 18 ≈ dc + 1 2 ac ! , where = 1 2 ! ! is the diode responsivity and = 1 is the diode differential resistance. However, when a nanoscale junction is illuminated with radiation of energy ℏ , the plasmonic response of the junction produces an a.c. voltage, opt , at frequency across the junction, and, in the limit of small a.c. amplitudes ( opt ≪ ℏ ), a quantum correction is required to consider photon-assisted tunneling. 19 In this semi-classical picture, 19 the diode differential resistance is and the diode responsivity is where = !" , = !" , and opt = ac as ℏ → 0. At dc = 0, !" = 70 ohm-cm 2 and !" = 0.4 V -1 for 1064 nm illumination (Fig. 3a), and these results are consistent with the values in Supplementary Table 1, which are based on applying a classical treatment to the illuminated dc curve ( Supplementary Fig. 11). The semi-classical rectified d.c. current can be expressed as = dc + 1 2 !" !" opt ! , and the semi-classical rectified d.c. diode voltage as D = −1 2 !" opt ! , which is valid when the rectenna is operating below its cutoff frequency. 20 Power generation, out , can be expressed as one-half the open-circuit voltage ( oc ) times one-half the short-circuit current ( sc ), which, in terms of basic device parameters is where !" and !" are at zero-bias conditions ( dc = 0). The maximum responsivity and optical voltage at unity quantum efficiency 19 are ℏ and ℏ , respectively, which reduces equation (11) to out = − ℏ ! 16 !" . Table 1. Dark and illuminated diode characteristics, measured open-circuit voltage and short-circuit current, and estimated energy conversion efficiencies for the devices in Fig. 3 of the main text. The statistical uncertainty in the extracted diode characteristics is approximately ±10% and approximately ±5% in the measured voltage and current. The illuminated diode resistance and responsivity are based on applying a classical treatment to the illuminated dc curve -the illuminated dc curve is shifted in this case such that = 0 at dc = 0. While this approach is only an approximation, it is useful when the range of voltages tested for dark dc characteristics is less than ±ℏ , and we find the agreement with equations (9) and (10) at dc = 0 to be within ±30%. The sample is heated at 11.2 W/cm 2 532 nm laser intensity, which is about 112 times more intense than the maximum illumination intensity in our rectenna response tests. Also shown is a device with a semi-transparent 30 nm top Al metal and no oxide layer. The red dashed line is the background voltage level. The halfway point between the positive and negative probe is approximately 10 µm from the negative probe.

Additional evidence for optical rectification
Supplementary Fig. 13. MWNT rectenna device under 1.5 AM solar illumination. The 2 nd derivative is computed from a 6 th -order polynomial fit to the illuminated current-voltage curve (from Supplementary Fig. 11c) to approximate the semi-classical correction. The agreement in the shape and sign of the voltage where the 2 nd derivative of the current-voltage crosses the abscissa with the data in Supplementary Fig. 11c is evidence for the photoresponse originating from optical rectification. 18