Fully Printed and Flexible Schottky Diodes Based on Carbon Nanomaterials Operating Up to 5 MHz

The capability to fabricate printed and flexible energy harvesting and conditioning circuits, over a large area and with low-cost techniques, is crucial to enable flexible and wearable electronics. Carbon nanomaterials show excellent electrical, optical, chemical, and mechanical properties for printed electronics, offering low-cost, and large-area functionality on flexible substrates. In the past few years, many efforts have been dedicated to the fabrication of printed transistors made with carbon nanomaterials, but very few works have been dedicated to diodes, which are fundamental circuit elements, often employed in energy harvesting systems. Here we report a simple and cost-effective approach for the fabrication of fully inkjet-printed Schottky diodes on Kapton and paper substrates using carbon nanotubes (CNT) and graphene. We demonstrate that both ohmic and Schottky contacts between printed nanotubes and graphene can be obtained with post-printing thermal treatments at different temperatures. The diodes thus fabricated work with low supply voltages, exhibit excellent mechanical stability and have a maximum operating frequency in the order of 5 MHz.

voltages at least in the high frequency (HF, 3-30 MHz) band, but also up to the ultra HF (UHF, 300-3000 MHz) band [3], [5], [6]. In particular, Schottky diodes are usually preferred for these applications because, as unipolar devices, they generally have shorter switching times (and can then work at HFs) and exhibit a lower voltage drop (which is particularly relevant in the case of energy scavenging) as compared, for example, to p-n junction diodes [7]. The challenge is then to find suitable materials (both semiconductors and metals) for the fabrication on flexible substrates and large-scale production.
In this article, we demonstrate a simple and effective method to fabricate low-cost, fully inkjet printed diodes on flexible substrate using graphene and single-walled CNT as contacts and p-type semiconductor, respectively. Device asymmetry is achieved by thermal annealing at different temperatures, which can be adjusted to obtain both an ohmic and a Schottky graphene-CNT contact. Devices fabricated on polyimide (Kapton) show good electrical properties, with an operating frequency of up to 5 MHz and excellent mechanical stability. Furthermore, we demonstrate the possibility of extending the proposed method to fabricate diodes on paper, which is an ideal substrate to enable sustainable flexible electronics due to its low cost, recyclability and biodegradability [33], [34].

II. MATERIALS AND METHODS
Kapton (from DuPont) and paper (PEL P60, from Printed Electronics Ltd.) were used as substrates. Commercial silver and PEDOT:PSS inks (nanoparticle silver ink, from Sigma-Aldrich and Clevios PH 1000, from Heraeus) were used to This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ print the metal contacts. The graphene contacts were instead printed starting from custom-made aqueous ink with a concentration of ∼2 mg · mL −1 , whose preparation details have been reported elsewhere [35]. A commercial 99.9% semiconducting single-walled CNT toluene solution (IsoSol-S100, from NanoIntegris) with a concentration of 0.2 mg · mL −1 in toluene and average diameter and length of the CNT of 1.4 nm and 1 μm, respectively, was used as semiconductor. A characterization of the inkjet printed network from this formulation is available in previous work by our group [36].
Prior to printing, Kapton was washed in deionized water and dried with nitrogen. All materials were deposited by inkjet printing using a Fujifilm Dimatix Materials Printer 2850, equipped with 10 pL cartridges. CNT on Kapton and paper were printed with a drop spacing of 20 μm and a single print pass. Graphene and PEDOT:PSS were printed on Kapton with a drop spacing of 30 μm and 20 print passes, while silver with a single pass and drop spacing of 40 μm. Each thermal treatment was carried out on a hot plate in air for 20 min. All the electrical measurements were performed under ambient conditions. The current-voltage (I -V ) characteristics were measured with a Keithley 4200A semiconductor characterization system. For the dynamic measurements, a function generator Siglent SDG2122X was used, with a value of the load resistor and capacitor of 100 M and 1 nF, respectively. These values were chosen to be much higher than the series resistance and capacitance of the device in order not to alter the measurement.

A. Inkjet Printed Devices With Different Metal Pairs
The devices have been inkjet printed on Kapton using the CNT network as the semiconductor, and considering different combinations of metals for the contacts. Kapton has been selected as the main substrate because of its low roughness, relatively high glass-transition temperature and high bendability [37], while inkjet printing has been chosen as the fabrication technique because it is a cost-effective, mask-less process which allows deposition of materials under ambient conditions, with good control over deposited volume and lateral resolution [38]. The main advantages of the proposed approach lie in its simplicity, low cost, and compatibility with flexible substrates, which are among the key requirements for printable and flexible electronics [5], [39]. Fig. 1(a) shows a schematic cross section of the devices, with metals 1 and 2 indicating the different materials used for the contacts, i.e., silver, graphene and poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS). Fig. 1 For an ideal p-type semiconductor-metal interface, the Schottky barrier height (SBH, φ B ) is predicted based on the alignment of energy levels by the Schottky-Mott rule [40] φ where I p is the ionization energy of the semiconductor (given by the sum of its electronic affinity and bandgap energy) and φ M the work function of the metal. Despite the different work functions of the metals [41], [42], [43], [44], [45], which should lead to different SBHs, our results show that all the I -V characteristics are symmetric, regardless of metal configuration. The complete symmetry of the measured I -V suggests that SBHs are virtually independent of metals. This may be ascribed to the pinning of the Fermi level, which could originate from the formation of surface states in the semiconductor bandgap at the junction with the metal [46]. If the interface state density is high, the Fermi level of the metal is pinned at a level within the semiconductor bandgap, which depends on the energy level of the interface states, φ I . In this case, (1) can be modified as follows [47]: where S = |∂φ B /∂φ M | is the pinning factor: if S = 1, there is an unpinned interface (Schottky limit), and (2) reduces to (1); if S = 0, there is maximum pinning of the Fermi level (Bardeen limit), and (2) becomes independent of the electrical properties of the metal. Our results suggest that the pinning is close to the Bardeen limit, in accordance with previous literature, where small S values (<0.1) have often been reported for interfaces with low-dimensional materials [48], [49], [50], [51]. This explains why SBHs values are rarely in agreement with the experimental results obtained from devices made with both conventional and low-dimensional materials [50], [52], [53], [54]. Fig. 2(a) and (b) shows the changes in the I -V characteristic of a device with graphene used for both contacts, obtained using different annealing temperature T A (from 50 • C to 275 • C). For these measurements, the device was initially cured at the lowest T A and subsequently measured at room temperature. Then it was cured at a higher T A and re-measured at room temperature, and so on. As expected, the behavior of the printed CNT-graphene contact significantly differs from that of a single nanotube-graphene contact investigate theoretically [55]. Thermal treatment leads to a change in the device resistance, which decreases as T A increases. This is likely due to the evaporation of the solvent (toluene, which has a low boiling point and therefore partially evaporates even at low T A ) and to binder degradation promoted by the thermal annealing, resulting in an improved carrier transport across CNT-CNT and CNT-graphene junctions [56], [57], [58]. As can be observed, T A has a significant influence on the nature of the contact between printed graphene and the CNT network, turning from the Schottky barrier into ohmic for T A above 200 • C.

B. Effect of the Annealing Temperature
To further investigate this effect, we have carried out fourprobe measurements. The dependence of both the semiconductor sheet resistance and the specific contact resistance of the printed graphene-CNT as a function of T A is reported in Fig. S1. Both quantities decrease significantly with T A , and the reduction is more pronounced for the contact resistance (about four orders of magnitude). The total resistance of the device is given by the contribution of the semiconductor resistance, R CNT , and the contact resistance, R C (the graphene resistance can be neglected, as shown in Fig. S2). Fig. 2(c) shows the relative weight of R C and R CNT over the total resistance for a one-square device (i.e., a device in which the length L and width W of the semiconductor are the same) for different T A . As can be observed, R c is the major contributor on the total resistance for low T A , while it becomes negligible as a result of annealing at relatively high temperatures (>200 • C).
The SBH in the case of thermionic emission can be expressed by the following formula [50]: where k is the Boltzmann's constant, T the temperature, q the elementary electric charge, A C the contact area, A * the Richardson constant, and I s the reverse saturation current (which can be extracted as the y-axis intercept of the ln(I ) versus V plot). An accurate evaluation of SBH is not possible, due to the uncertainty of the value of A * for a network of printed CNT. Regardless of the actual value of φ B , however, is it possible to evaluate its relative variation as a function of the annealing temperature. Fig. 2(d) shows the normalized SBH (φ B /φ B0 , where φ B0 is the SBH for T A = 50 • C) as a function of T A . Consistently with what has been observed for the contact resistance, we notice a significant reduction of the SBH as T A increases.

C. Inkjet Printed Diodes on Kapton
We exploit the dependence of the SBH on the annealing temperature to demonstrate in-plane, fully inkjet-printed rectifying devices by combining networks of CNT and graphene contacts treated at different annealing conditions. The fabrication starts by printing one graphene contact on Kapton (labeled as contact 1) and a printed CNT network (N1), as shown in the inset of Fig. 3(a). A thermal treatment at 250 • C follows, which makes the printed graphene-CNT contact ohmic, as previously demonstrated. The second graphene contact (contact 2) is then printed together with the second region of the CNT network (N2), which slightly overlaps region N1 [inset of Fig. 3(a)]. The fabrication process ends with a thermal treatment at 150 • C. This annealing temperature results in a good compromise, as it allows to get a barrier high enough to obtain an acceptable rectification ratio while reducing the series resistance introduced by N2. The latter is a crucial aspect as N2 is the part of the device that introduces the highest series resistance (along with the relative contact resistance): its reduction is therefore fundamental in order to reduce the total series resistance of the diode, R s . For the same reason, it is also important to shorten the length of N2 (L 2 ) or to enlarge its width (W 2 ). The interface between the N1 and N2 regions is ohmic, as shown in Fig. S3.
The I -V characteristic of a device fabricated following the described procedure is reported in Fig. 3(a), both in semilogarithmic and the linear scale. The device is biased between contact 1 (anode) and contact 2 (cathode) and has an overall network width and length of 250 and 150 μm, respectively. A clear rectifying behavior can be observed, with a rectification factor (defined as the ratio between the forward current evaluated at a certain voltage V X > 0 and the reverse current evaluated at −V x ) of ∼10 2 at 4 V. The polarity is consistent with that expected in the case of a p-type semiconductor-metal junction. A fitting of a diode characteristic using the Shockley equation is reported in Fig. S4.
The height profile of a CNT network printed on SiO 2 is shown in Fig. S5. The average thickness t is about 25 nm, in line with those reported in the literature for printed networks [59], [60]. Considering this thickness, the forward current density [J = I/(Wt)] for the device whose I -V characteristic is shown in Fig. 3(a) is of the order of 5 A · cm 2 at 4 V (see Fig. S6). In Fig. S7 the J -V characteristics of four different devices are reported.
The printed diodes exhibit negligible hysteresis and can operate with moderate supply voltages (of the order of a few volts). In addition, the adopted method allows using the same metal for both contacts, while leveraging printed graphene, which is a low-cost material, with good electric conductivity and excellent mechanical properties [61], [62], [63]. Also considering the high flexibility reported for CNT networks [64], these devices are particularly promising for flexible applications. To confirm this, we have carried out bending measurements of the printed diodes on Kapton. Tensile stress is applied to the devices by wrapping the substrate on cylindrical supports with different radii (r ): 5, 3, and 2 mm. The I -V characteristic measured under different bending conditions are reported in Fig. 3(b). There are no major changes under the different bending conditions, although for the smaller investigated value r = 2 mm, there is a slight reduction in the forward current and an increase in the reverse current. The effect, however, is reversible since the characteristic returns to its original values once the strain is removed, demonstrating very good stability of the diodes against mechanical bending.

D. Dynamic Response
One of the most important figures of merit for determining the performance of a diode is its maximum operating frequency [3], [5]. Different figures of merit exist to define the maximum operating frequency of a Schottky diode. Among them, one of the most frequently used is the 3-dB cutoff frequency, f c , which is usually extracted by inserting the diode in the half-rectifying configuration shown in the inset of Fig. 4(a) [21], [65]. The input generator provides a single harmonic signal v in at frequency f and amplitude V IN [v in (t) = V IN sin(2πft)]. R L and C L are the load resistor and capacitor, respectively, and are chosen to be much higher than those of the diode, in order not to affect its frequency response. f c is the frequency at which the output voltage (V OUT , measured with a multimeter) is attenuated by 3 dB with respect to the maximum V OUT (that is, V OUT extracted for low frequencies). Fig. 4(a) shows the measured V OUT for a diode printed on Kapton as a function of the frequency of the input signal. The 3-dB cutoff frequency is found to be ∼1.4 MHz.
It is further possible to increase the operating frequency range by adjusting the device dimensions. The cutoff fre-quency is, indeed, inversely proportional to the diode series resistance [65]. As mentioned, R s is primarily limited by the printed region N2 and the relative contact. It is therefore possible to reduce R s by modifying the geometry of N2. Fig. 4(b) shows the I -V characteristics in the forward region for two devices with the same L 2 but different W 2 (200 and 1000 μm). As expected, the device with higher W 2 exhibits lower R s . This reflects in an increase of the 3-dB cutoff frequency, as shown in the Bode Fig. 4(c). f c reaches a value close to 5 MHz for the wider device, which is within the HF range. This value is in line with or better than several organic and inorganic solution-processed diodes [15], [16], [20], [66], although not comparable to the best results in literature [18], [25], [67]. With further optimizations, the cutoff frequency can be increased, for example, with the goal of achieving 13.56 MHz, a frequency widely used for RFID tags [68].

E. Inkjet Printed Diodes on Paper
Finally, we show that the proposed method can also be used for the fabrication of printed diodes on paper, which is a porous substrate with a higher surface roughness compared to plastic substrates. Moreover, the relatively high annealing temperatures used to cure the devices on Kapton are not compatible with a thermally sensitive substrate such as paper (the employed paper can withstand a maximum temperature of about 120 • C). However, it is necessary to take into account that the properties of paper are rather different from those of a plastic substrate such as Kapton. This is reflected in a different electrical conduction between devices printed on paper and on Kapton. Fig. 5(a) and (b) show, respectively, the effect of T A on the I -V characteristics and total resistance (R T ) for a onesquare device on paper (formed by a unique CNT network). As can be observed from the comparison with Fig. 2, currents are higher (and resistances lower) for devices on paper with the same dimensions. This may be due to the fact that paper absorbs some of the solvent from the ink, which therefore has less impact on conduction at low annealing temperatures. Fig. 5(c) shows the I -V characteristic of a diode obtained with the same previously described procedure, but with a single heat treatment at 120 • C after printing contact 1 and N1, while contact 2 and N2 are untreated. It can be noticed that the diode on paper exhibits a significantly larger hysteresis than those on Kapton. This might be due to the presence of traps at the interface between the CNT network and the rough paper substrate, as well as to the reduced annealing temperature. Other post-processing treatments could be beneficial and allow to treat the device in a way compatible with the substrate. For example, fast laser and photonic annealing have been successfully employed to cure printed materials on low glasstransition temperature substrates [62], [69]. However, even in this case the device exhibits good electrical properties with a rectifying factor >10 2 at 4 V. In addition, diodes on paper have a rectification factor in the order of 10 2 even in the ±1 V voltage range [see Fig. 5(d)], and are therefore suitable for operating at very low voltages. The I -V characteristics of four different diodes in the ±1 V range are shown in Fig. S9. We have also carried out bending measurements for the diode on paper, reported in Fig. S10, which show good stability of the characteristics down to bending radii of 5 mm.

IV. CONCLUSION
We have demonstrated a simple, low-cost approach that exploits the dependence of the SBH on the annealing temperature to demonstrate in-plane, fully inkjet-printed rectifying devices by combining networks of CNT and graphene contacts treated at different temperatures. The devices printed on Kapton have shown a rectification ratio up to 10 2 , operating at voltages of a few volts, stability against substrate bending down to 2 mm, and maximum operating frequency in the order of 5 MHz. We have also demonstrated diodes on paper fabricated with the same method that can operate with a voltage of the order of 1 V.
Present results are relevant for the development of a broad range of applications that require flexible, printed, and lowcost diodes.