High-Performance D-Band Frequency Multiplier Using Aligned Carbon Nanotube Schottky Barrier Diodes

Abstract

Millimeter-wave (mmWave)/terahertz (THz) devices relying on conventional semiconductor technologies face significant performance bottlenecks, constraining their use in next-generation electronic systems. To address these challenges, this work demonstrates high-performance THz Schottky barrier diodes (SBDs) based on aligned carbon nanotube (ACNT) arrays, and the realization of a D-band second-harmonic frequency multiplier. The ACNT-SBDs exhibit superior electrical and radio-frequency (RF) characteristics, achieving a forward current density of 0.14 mA·μm⁻¹ at −1.3 V and an intrinsic cutoff frequency (f_C) of 506 GHz. The developed small-signal model of diodes shows close agreement with measurements, with S-parameter relative errors below 0.7% from 100 MHz to 67 GHz. The implemented 154 GHz D-band multiplier achieved a maximum output power of −18.97 dBm and a minimum conversion loss of 27.92 dB, outperforming previously reported frequency multipliers based on carbon nanotubes or two-dimensional (2D) materials. This study not only establishes the outstanding high-frequency response, nonlinear efficiency, and integration potential of ACNT-based devices but also provides a promising technical pathway for future THz communication and sensing applications.

1. Introduction

Wireless communication, imaging, and sensing systems are rapidly advancing towards higher operating frequencies and greater integration levels. The mmWave band (30–300 GHz) offers compelling advantages for these applications, including high spatial resolution, system miniaturization, and adaptability to complex environments. However, its practical implementation faces significant challenges at both the device and circuit levels [1]. The performance of solid-state mmWave frequency multipliers is fundamentally constrained by insertion loss, thermal management, and reliability limitations associated with conventional semiconductor technologies and their native substrates. These constraints significantly reduce output efficiency and hinder the practical realization of highly integrated systems at mmWave frequencies [2]. Consequently, further improvement in mmWave and THz frequency multipliers relies not only on circuit-level optimization but, more critically, on breakthroughs in the intrinsic electrical properties of nonlinear devices. An ideal nonlinear device should exhibit high carrier transport velocity to enable efficient frequency conversion and stable operation under high-frequency conditions.

Carbon nanotubes (CNTs), with their quasi-one-dimensional charge transport, present a promising alternative due to several superior intrinsic electrical properties. Their high carrier mobility, high saturation drift velocity, and extremely low intrinsic capacitance provide a strong foundation for high-frequency nonlinear applications [3,4,5,6]. Carbon-based electronic devices have been extensively explored in flexible electronics [7,8], high-frequency signal transceivers [9,10,11], and high-speed information processing systems [12,13,14]. Although low-dimensional material-based SBDs have demonstrated notable progress in the gigahertz (GHz) frequency range in recent years, their practical operation above 100 GHz is still a challenge [15,16]. By comparison, high-purity ACNT arrays offer a realistic and scalable route toward high-frequency, high-speed, and low-power electronic systems [17,18]. Nevertheless, most reported CNT-based frequency conversion devices are still confined to the sub-mmWave regime and suffer from low conversion efficiency [19,20,21], falling short of the stringent requirements for emerging fifth-generation (5G) and future sixth-generation (6G) communication systems in terms of operational frequency and power efficiency.

In this work, we address this gap by developing and characterizing high-performance Schottky barrier diodes based on aligned carbon nanotube arrays (ACNT-SBDs), and successfully implementing a D-band frequency multiplier. The fabricated ACNT-SBD (W = 60 μm) achieves a forward current density of 0.14 mA·μm⁻¹ at a bias voltage of −1.3 V and exhibits an intrinsic cutoff frequency (f_C) as high as 506 GHz, outperforming the SBD devices based on 2D materials and oxide semiconductors. A small-signal model was established, accurately de-embedding the intrinsic device behavior from the parasitic effects of the ground–signal–ground (GSG) pads. This model exhibited excellent accuracy, with a relative error between measured and simulated S-parameters of less than 0.7% across the 100 MHz to 67 GHz range under multiple bias conditions. Leveraging this optimized ACNT-SBD, we designed and implemented a 154 GHz D-band frequency multiplier integrating passive harmonic filtering network. The multiplier delivered a maximum output power of −18.97 dBm with a minimum conversion loss of 27.92 dB, outperforming previously reported multipliers based on CNT transistors and 2D materials. This work not only establishes the outstanding high-frequency response, nonlinear efficiency, and integration potential of ACNT-based devices but also provides a promising technical pathway for future THz communication and sensing applications.

2. Materials and Methods

ACNT array film with a density of 230 CNT·μm⁻¹ was formed on a quartz substrate using the dimension-limited self-alignment (DLSA) method [22], and the corresponding scanning electron microscopy (SEM) image is shown in Figure 1a. Prior to device fabrication, interface pretreatment was carried out, consisting of an yttrium (Y) oxide cleaning process followed by high-temperature annealing. Specifically, a 3 nm thick Y metal layer was deposited onto the ACNT arrays by electron-beam evaporation (EBE). The deposited sample was then annealed on a hot plate at 300 °C for 30 min to fully oxidize the Y layer into yttrium oxide (Y₂O₃). The resulting Y₂O₃ layer was then etched in dilute hydrochloric acid for 20 min and rinsed with ultrapure water until a clean surface was obtained. Subsequently, the sample was annealed at 600 °C for 3 h in an inert N₂/H₂ mixed atmosphere to remove residual polycarbazole (PCz) molecules wrapping the CNTs and to improve the contact quality between the CNTs and metal electrodes.

A three-dimensional schematic of the complete device structure is shown in Figure 1b. The device active region was defined using electron-beam lithography (EBL) combined with oxygen plasma etching. Titanium/gold (Ti/Au, 20/60 nm) and palladium/gold (Pd/Au, 20/60 nm) metal stacks were sequentially deposited by EBE to serve as the Schottky anode and ohmic cathode, respectively. The detailed structure of the device core region is illustrated in Figure 1c. Standard two-port GSG probe pads were fabricated using photolithography and EBE for subsequent direct-current (DC) characterization and high-frequency measurements.

The sample covered with the ACNT array film was annealed in a tube furnace (Thermo Scientific Lindberg/Blue M Moldatherm 1100 °C, Thermo Fisher Scientific, Waltham, MA, USA). SEM images of the ACNT array film and ACNT-SBD were obtained using a Sigma 300 microscope (ZEISS, Oberkochen, Germany). Electrical characteristics of the ACNT-SBDs were measured at room temperature using a Keithley 4200 semiconductor characterization system (Keithley Instruments, Cleveland, OH, USA) combined with a probe station (MPI TS200-SE, MPI Corporation, Munich, Germany). Patterning of the ACNT-SBDs was carried out using an EBL system (Raith 150, Raith GmbH, Dortmund, Germany), and metal deposition was performed using an EBE system (Kurt J. Lesker Company, Jefferson Hills, PA, USA).

3. Results and Discussion

3.1. Electrical and RF Characterization of ACNT-SBDs

The electrode spacing was fixed at 150 nm, and devices with four different channel widths (W = 50, 60, 100, and 200 μm) were fabricated. Figure 2 presents the I–V characteristics of the ACNT-SBDs. Among them, the device with a channel width of 60 μm achieves a forward current density of 0.14 mA·μm⁻¹ at a bias voltage of −1.3 V. As the channel width increases, the metal–CNT contact area correspondingly expands, leading to an increased number of parallel carrier transport channels within the active region and, consequently, enhanced current conduction capability.

The forward current–voltage characteristics were analyzed using the thermionic emission theory, expressed as follows

$$I=I_s\left[exp\left({\displaystyle \frac{q(V-I{R}_s)}{nkT}}-1\right)\right],$$

(1)

where the I, I_s, q, V, R_s, n, k, and T denote the total current, reverse saturation current, elementary charge, applied voltage, series resistance, ideality factor, Boltzmann constant, and absolute temperature, respectively. The reverse saturation current I_s can be further defined as follows

$$I_s=A{A}^{\ast }{T}^{2}exp\left(-{\displaystyle \frac{q{\Phi }_B}{kT}}\right),$$

(2)

where A is the effective diode area, A* is the effective Richardson constant, and Φ_B is the effective Schottky barrier height. By fitting the exponential region of the forward I–V curve, the ideality factor n and the effective Schottky barrier height Φ_B were extracted. The extracted parameters are summarized in

Table 1. Extracted parameters of ACNT-SBDs with different channel widths.

Extracted Parameter	W = 50 μm	W = 60 μm	W = 100 μm	W = 200 μm
n	3.689	3.794	3.556	3.161
ΦB (eV)	0.227	0.211	0.227	0.265

.

As summarized in Table 1, the extracted ideality factors deviate noticeably from unity, indicating that the carrier transport in the ACNT-SBDs cannot be solely described by ideal thermionic emission or diffusion mechanisms [23]. Meanwhile, the effective Schottky barrier heights extracted from the forward I–V characteristics lie in the range of 0.211–0.265 eV, consistent with reported values for metal–carbon nanotube contacts. The variation in Φ_B among devices with different channel widths is mainly associated with the non-uniform CNT/metal interface, including contact inhomogeneity and local variations in CNT properties.

Variations in device width also induce systematic changes in the on-state series contact resistance (R_s-on) and the off-state junction capacitance (C_j-off), as shown in Figure 3. Under a fixed S, the increase in W introduces multiple parallel transport channels, which significantly reduces the effective series resistance according to the parallel resistance model. The Schottky junction capacitance originates from the space-charge region formed at the metal–semiconductor interface, and its magnitude is positively correlated with the effective contact area. It can be approximately described by a parallel-plate capacitor model,

$$C={\displaystyle \frac{{\epsilon }_0{\epsilon }_{r}A}{d}} ,$$

(3)

where A is the effective contact area, ε₀ is the vacuum permittivity, ε_r is the relative permittivity of the semiconductor, and d is the width of the space-charge region. As the device width increases, the effective contact area A of the Schottky junction increases accordingly, while the space-charge width d remains nearly constant under a fixed bias, resulting in a monotonic increase in junction capacitance. In addition, the enlarged electrode dimensions introduce extra parasitic capacitance, further amplifying the increase in C_j-off. The high-frequency performance of a SBD can be evaluated by its intrinsic f_c, defined as follows

$$f_{\mathrm{c}}={\displaystyle \frac{1}{2\pi R_{\mathrm{s}\text{-}\mathrm{o}\mathrm{n}}{C}_{\mathrm{j}\text{-}\mathrm{o}\mathrm{f}\mathrm{f}}}} ,$$

(4)

Figure 3 summarizes the extracted f_c for devices with different W. The device with a channel width of 60 μm exhibits an f_c as high as 506 GHz.

Figure 4 further compares the f_c achieved in this work with those of diodes based on CNTs, 2D materials, metal oxides, and organic semiconductors [23,24,25,26,27,28,29,30,31,32,33,34,35,36]. Benefiting from the exceptionally high carrier mobility of ACNTs, the present device demonstrates superior high-frequency characteristics, highlighting its strong potential for THz applications.

Therefore, the channel width directly modulates the number of carrier transport channels and the effective contact area, thereby governing the on-state resistance, junction capacitance, and overall high-frequency response of the device. These results provide important guidance for the structural optimization of ACNT-SBDs. In particular, for RF applications, the f_c is jointly determined by R_s-on and C_j-off; minimizing a single parameter alone is insufficient to achieve optimal device performance. Instead, a balanced design of geometric parameters, including W and S, is required to simultaneously optimize electrical conduction and frequency response.

3.2. Modeling of ACNT-SBDs

Based on the measured two-port S-parameter data, a corresponding small-signal model was established and the core parameters were extracted, with the model topology illustrated in Figure 5. The model consists of two main components: intrinsic core module and parasitic module. The intrinsic core module describes the carrier transport behavior and junction capacitance characteristics of the CNT–metal Schottky junction, while the parasitic module accounts for high-frequency non-ideal effects introduced by the GSG pads. Through optimized design, the GSG pads were engineered to minimize signal coupling and scattering during high-frequency measurements. The parasitic parameters extracted using an open–through de-embedding structure are L_p ≈ 23.7 pH, C_p ≈ 0.42 fF, C_pad ≈ 4.6 fF, and a series resistance of about 0.1 Ω.

Within the intrinsic core module, R_j represents the Schottky junction resistance, C_j denotes the Schottky junction capacitance, and R_s corresponds to the ohmic contact resistance. In addition, an extra ohmic capacitance C_s is introduced to describe non-ideal contact behavior arising from polymer residues remaining from the CNT sorting process. The capacitance C_s decreases primarily with the reduction in the effective electrode area (channel length × width) and is nearly independent of the applied bias voltage. To further accurately capture the intrinsic properties of the CNT, a parallel coupling capacitance C_Q is included to represent the electrostatic capacitance of the ACNTs and inter-tube coupling effects, together with a resistance R_Q to model coupling capacitance-related losses induced by the ACNTs under high-frequency operation.

Figure 6 compares the measured S-parameters with the simulated results for devices with different channel widths under bias voltages of −0.5 V, 0 V, and 0.5 V. Across the entire measured frequency range from 100 MHz to 67 GHz, excellent agreement is observed between the experimental data and model simulations. The model effectively captures the combined influence of the bias-dependent junction capacitance C_j and the ohmic capacitance C_s, enabling the simulated curves to accurately follow the measured S-parameter variations with bias voltage and thus precisely reflect the high-frequency transmission and reflection characteristics of the devices. It should be noted that the proposed small-signal model is bias-dependent, with the parameters of the diode core extracted under different applied bias conditions, while the model structure itself remains scalable through geometric dimension scaling.

To quantitatively evaluate the applicability of the small-signal model, an error analysis was performed. Figure 7 presents the frequency-dependent relative errors between the measured and simulated S₁₁, S₁₂, S₂₂, and S₂₁ parameters for devices with different widths under multiple bias conditions (0 V and ±0.5 V). Across the full frequency range, the S-parameter errors for all devices remain at low levels under various bias conditions. In the low- to mid-frequency transition region (100 MHz–10 GHz), device operation gradually shifts from DC/quasi-static transport to small-signal alternating current (AC) response. In this regime, residual parasitic effects associated with the measurement ports—such as bias networks, cable losses, and non-ideal probe contacts—are amplified in the reflected signals, resulting in a moderate increase in normalized error. In the stable mid-frequency region, the relative S-parameter error remains approximately 0.2%, indicating that the proposed model accurately captures the essential RF behavior of the devices. As the frequency further increases, the error gradually rises, primarily due to increased insertion loss intrinsic to the devices at high frequencies, as well as uncertainties introduced by probe contact variation, calibration drift, and system noise during high-frequency measurements. These factors collectively amplify deviations in both transmission and reflection parameters at higher frequencies; nevertheless, the overall error remains below 0.4%, demonstrating excellent modeling accuracy. Consequently, this scalable model enables the effective design and simulation of impedance matching networks for CNT diode circuits.

3.3. D-Band Frequency Multiplier Based on ACNT-SBD

As discussed in Section 3.1, the device with a channel width 60 μm, which achieves an optimal trade-off between conduction performance and frequency characteristics, was selected for the fabrication of the D-band frequency multiplier. In this design, a zero-bias ACNT-SBD is employed as the nonlinear core device. This approach not only exploits the optimal nonlinear characteristics of the diode under zero-bias operation but also simplifies both fabrication and measurement complexity. From a circuit perspective, conventional frequency multipliers typically consist of three key building blocks: a matching network, a SBD active unit, and filtering networks. In this work, the operating frequency of the frequency multiplier is extended to 154 GHz. By comparison, previously reported bipolar transistor-based frequency multipliers utilizing ACNT arrays exhibited a maximum output frequency of 40 GHz with a conversion loss as high as 36 dB [19,20,21].

Figure 8a illustrates the topology of the proposed second-harmonic (×2) frequency multiplier circuit operating at 154 GHz. Unlike conventional designs in which the matching network and filter are implemented as separate functional blocks, an integrated passive harmonic filtering network is introduced in this work. This integrated network simultaneously fulfills three functions: effective suppression of the fundamental frequency component, efficient extraction of the second harmonic, and impedance matching for the nonlinear device. By adopting a harmonic impedance focusing technique, the proposed design achieves more precise circuit control while significantly reducing the chip footprint, thereby improving the utilization efficiency of CNT material. Figure 8b shows an optical micrograph of the fabricated circuit on wafer. The circuit metallization was realized by EBE of Ti/Au. To mitigate skin effect-induced losses in the mmWave band [37], the metal thickness was increased to 500 nm. Meanwhile, the quartz substrate was thinned to 100 μm, and a backside ground metallization was also deposited by EBE to serve as the reference ground.

Figure 8c illustrates the mmWave measurement setup used for characterizing the D-band frequency multiplier. The input signal was generated by a vector network analyzer (N5247B, Keysight Technologies, Santa Rosa, CA, USA) and subsequently up-converted by a mmWave frequency extender (N5293A-01, Keysight Technologies, Santa Rosa, CA, USA). After amplification by a D-band power amplifier, sufficient drive power in the 75–110 GHz frequency range was delivered to the device under test. Prior to device measurements, the input signal path was calibrated using a power meter and power sensor, taking into account the losses introduced by coaxial cables, the frequency extender, and the GSG probe, thereby determining the actual input power at the probe tip. For output power measurements, the device was contacted using GSG probes, and the output signal was routed through the probe and a waveguide-to-coaxial transition to a power meter (E4416A, Keysight Technologies, Santa Rosa, CA, USA). The total insertion loss of the output signal path was calibrated in advance, including the losses associated with the GSG probe and the waveguide transition. The reported output power was obtained by correcting the power meter readings with the calibrated transmission losses.

Figure 8d presents the measured output power and conversion loss of both the D-band frequency multiplier circuit and the standalone ACNT-SBD as functions of input power. The input frequency was set to 77 GHz, corresponding to a second-harmonic output frequency of 154 GHz. As the input power increases, the second-harmonic output power of both the circuit and the device exhibits an approximately linear increase. Notably, the CNT-based frequency multiplier consistently delivers higher output power across the entire input power range. The proposed frequency multiplier achieves a maximum output power of −18.97 dBm and a minimum conversion loss of 27.92 dB, whereas the standalone ACNT-SBD (W = 60 μm) without circuit optimization exhibits a maximum output power of only −30.2 dBm and a minimum multiplication loss of 38.34 dB, with all reported results obtained from measurements. These results not only confirm the effectiveness of the proposed circuit design but also directly demonstrate the strong nonlinear frequency conversion capability of ACNT-SBDs in the mmWave regime. To the best of our knowledge, this work represents the first experimental realization of a D-band frequency multiplier based on ACNT-SBDs.

Figure 9 compares the performance of the proposed frequency multiplier with previously reported frequency multipliers based on CNT transistors and other 2D materials [15,16,19,38,39,40,41,42]. The present work achieves a higher output frequency together with competitive conversion loss, highlighting the advantages of ACNT-SBD for scalable mmWave and sub-THz frequency generation.

4. Conclusions

In conclusion, this work presents a systematic study of ACNT-SBDs, covering device fabrication, DC and RF characterization, small-signal modeling, and circuit-level implementation. ACNT-SBDs with a fixed electrode spacing and varying channel widths were fabricated, among which the 60 μm-wide device exhibited the best overall performance, delivering a forward current density of 0.14 mA·μm⁻¹ at −1.3 V and an intrinsic cutoff frequency (f_C) of 506 GHz. These results confirm the excellent high-frequency capability of ACNT-SBDs enabled by the high carrier mobility of CNTs. A physics-based small-signal model incorporating both intrinsic device behavior and parasitic effects was established and experimentally validated, showing excellent agreement with measured S-parameters from 100 MHz to 67 GHz under different bias conditions, with relative errors consistently below 0.7%. A 154 GHz second-harmonic D-band frequency multiplier based on a zero-bias ACNT-SBD and an integrated passive harmonic filtering network was successfully demonstrated. The proposed multiplier delivers a maximum output power of −18.97 dBm and a minimum conversion loss of 27.92 dB, outperforming previously reported frequency multipliers based on CNT transistors and 2D materials. Notably, this work constitutes the first experimental demonstration of a D-band frequency multiplier enabled by ACNT-SBDs.

Overall, this study highlights the strong high-frequency response, nonlinear conversion efficiency, and integration potential of ACNT-based devices, providing a viable technological route toward future THz communication and sensing systems.