Introduction

Terahertz traveling wave tubes (TWTs) have broad application prospects in wireless communication, radar detection, space technology, biomedicine, etc1,2,3,4due to their wide band, high speed, high security, strong penetrability and precise directionality. A wider operating band can obtain a higher data transmission rate, and higher output power can bring wider coverage area and higher signal transmission quality and efficiency5. Thus, terahertz TWTs with wide bandwidth and high output power are promising for 6G applications. A key factor in developing high-performance and long-lifetime terahertz TWTs is the electron source, which requires large emission current density and high stability. However, the widely used thermionic cathode electron source6,7operates at high temperature, leading to deformation and instability in terahertz TWTs8. Additionally, thermionic cathodes have inherent drawbacks, such as slow response, large and complex structures, which contradict the trends towards miniaturization and instant startup in TWT development.

Field emission cathodes, also known as cold cathodes, offer advantages such as cold emission, instantaneous start-up, and easy of miniaturization and integration9. Additionally, cold cathodes can theoretically provide a high current density of 107 A/cm2 10making them a type of promising electron source for terahertz TWTs. Early research on cold cathode TWTs primarily focused on the Spindt cathode10,11,12,13due to its high emission current density. However, the fabrication process for Spindt cathodes is complex and costly, and their stable operation requires an extremely high vacuum14. As a result, several technical challenges associated with Spindt cathodes still need to be addressed.

Another ideal field emission electron source for terahertz TWTs is the carbon nanotubes (CNTs)-based cold cathode, which features a low turn-on field, high stability, high field emission current density, and simple fabrication processes15. Most reported electron guns or TWTs with CNTs cold cathodes are based on grid-controlled structures9,16,17,18,19,20. While these structures help reduce the extraction voltage applied to the cold cathode, they also increase the instability of devices. Although recent report has reduced the simulated interception rate of the grid structure to around 15%19, it still cannot completely avoid the problem of intercepting emitted electrons, posing a risk of grid burnout. Li et al. designed a grid-free gun based on a CNT cold cathode, which was employed in an X-band TWT21, achieving a high electron transmission ratio of about 86%.

However, all the aforementioned research on cold cathode TWTs has been focused on low frequencies. While there are some reports on the application of cold cathodes in terahertz gyrotrons22,23, backward wave tubes24, and extended interaction oscillators25,26, there are almost no related reports on terahertz TWTs based on cold cathodes, except for a few recent reports on cold cathode electron guns for terahertz TWTs27. This is because the beam-wave interaction length of TWT is longer compared to the aforementioned devices, and the size of terahertz devices is very small, which make it more challenging to maintain good electron beam transmittance, thereby imposing higher demands on the electron beam focusing performance and field emission stability of the cold cathode.

In this paper, a miniaturized terahertz TWT based on a stable cold cathode electron source is studied in detail. The enhanced single-walled CNTs (SWCNTs) cold cathode is prepared, and the embedded-cathode structure is designed, both of which effectively support the application in terahertz TWTs. This paper is organized as follows. Firstly, the SWCNTs cold cathode with low turn-on field and enhanced emission stability prepared by the improved screen-printing technology is presented. Then, a grid-free electron gun with the embedded SWCNTs cold cathode is designed, which can significantly improve the focusing performance. The grid free structure avoids the problem of burning grid. Combined with the periodic permanent magnet (PPM) focusing system, the beam waist radius is 0.016 mm with 100% electron beam transmittance. Next, a G-band folded waveguide TWT with the SWCNTs cold cathode is studied. The simulated output power is 807 mW at 220 GHz and the corresponding gain is 10.6 dB when the input power is 70 mW. The designed cold-cathode terahertz TWT is expected to be used in terahertz communication, such as 6G. Finally, a concise conclusion is given at the end.

Field emission test of the SWCNTs cathode

The SWCNTs is a type of ideal field emission material because of its high aspect ratio, good electron emission stability, and superior mechanical and electronic properties28. To enhance emission performance and promote commercial production to some extent, the SWCNTs cold cathode is prepared using the improved screen-printing method with a silver paste buffer layer29. Unlike the conventional screen-printing method that mixes CNTs with the organic binder paste30,31, this approach introduces a silver paste buffer layer to connect the SWCNTs emitters and the substrate, which does not require mixing SWCNTs with silver paste, and can also address the issue of poor adhesion between SWCNTs and the substrate. On the one hand, the SWCNTs emitters are above the silver paste buffer layer with only partially body embedded into the silver paste, ensuring that the emitters are not covered by the silver paste, thus lowering the turn-on field. On the other hand, the partially body of SWCNTs embedded in the silver paste can form good contact with the substrate, which is conducive to reducing contact resistance, enhancing the adhesion of SWCNTs on the substrate, and improving the emission stability.

Field emission measurements are conducted in a vacuum chamber with a base pressure of approximately 1 × 10−4 Pa. Both DC and pulsed voltage (with the frequency of 10 Hz and pulse width of 1 ms) are applied to evaluate the field emission performance. The turn-on field, corresponding to the emission current density of 10 µA/cm2, is tested under DC mode, while the maximum emission current is measured under pulse mode. The surface morphology of the SWCNTs cathode is characterized using scanning electron microscopy (SEM).

The field emission characteristics are analyzed using the Fowler–Nordheim (F-N) theory, as described by32:

$$J=A\frac{{{{(\beta E)}^2}}}{\varphi }{e^{ - \frac{{B{\varphi ^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0pt} 2}}}}}{{\beta E}}}}$$
(1)

where J is the emission current density, E is the electric field at the cathode surface, β is the field enhancement factor, and A and B are constants (A = 1.54 × 10−6A·eV·V-2 and B = 6.83 × 103 V·eV−3/2·µm−1). φ represents the work function of the cathode.

Taking the natural logarithm of Eq. (1) results in the following linear equation:

$$\ln ({J \mathord{\left/ {\vphantom {J {{E^2}}}} \right. \kern-0pt} {{E^2}}})=\ln (\frac{{A{\beta ^2}}}{\varphi }) - \frac{{B{\varphi ^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0pt} 2}}}}}{{\beta E}}$$
(2)

The plot of ln(J/E2) versus 1/E, derived from the F-N Eq. (2), results in a straight line known as the F-N plot. This straight line indicates that the electrons are emitted via the quantum tunneling process.

Figure 1 shows the field emission experimental results of the SWCNTs cold cathode. The diameter of the printed SWCNTs cathode is 0.2 mm, and the distance between the cathode and anode is set to 0.3 mm. The cathode is applied with negative bias and the anode is grounded during the tests. The turn-on field of the SWCNTs cathode is as low as 0.78 V/µm, with the field enhancement factor reaching 8500. After repeated tests, the SWCNTs cathode demonstrates good repeatability and stability, as shown in Fig. 1a. The corresponding F-N plot is presented in Fig. 1b. The maximum emission current density is approximately 11 A/cm2 under pulsed voltage excitation, as shown in Fig. 1c, illustrating its strong potential in TWT applications. The current density remains stable without significant degradation at about 20 mA/cm2 during the test, as shown in Fig. 1d. While the emission stability at the maximum emission current density still degrades over time, and the long-period stability needs to be improved in future work. Table 1 compares the field emission performance of CNTs cold cathodes prepared by different cathode techniques. As can be seen, the SWCNTs cold cathode of this work has advantages in comparing the turn-on field and threshold field. The emission stability of the CNTs cold cathodes exhibit a decreasing trend with the increase of emission current density. Compared with other cold cathodes in Table 1., the SWCNTs cold cathode in this study has poor emission stability at high current density. This may be due to the low vacuum degree in this work, which results in much damage to SWCNTs caused by ion bombardment. On the other hand, under high current density, the cathode thermal effect is significant33. Both two factors are detrimental to emission stability. In the next step, we will improve the emission stability of SWCNTs cold cathodes under high current density, such as increasing the vacuum degree, exhaust under high-temperature and high-pressure, and designing the cold cathode with heat dissipation structures, etc.

Fig. 1
Fig. 1
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Field emission test results of the SWCNTs cathode. (a) The current density (J)- electric field (E) plot. (b) The corresponding F-N plot. (c) The maximum emission current density (Jmax). (d) Field emission stability.

Table 1 Field emission performance comparison of CNTs cold cathodes prepared by different cathode techniques.
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To observe the distribution of SWCNTs on the cathode surface over a relatively large range, the SEM image with a scale of 1 μm is shown in Fig. 2a. The image reveals that the surface is covered with pure SWCNTs, free of impurities, and features a high aspect ratio, thus contributing to reducing the operating voltage. To better observe the SWCNTs after the field emission tests, the SEM image with a scale of 5 μm is provided in Fig. 2b. This image shows that the SWCNTs remain firmly in contact with the substrate due to the strong adhesion of the silver paste buffer layer, which is beneficial for achieving high emission current density and stable emission performance.

Fig. 2
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SEM images of the SWCNTs cold cathode. (a) Before field emission test. (b) After field emission test.

Design of the grid-free electron gun with embedded SWCNTs cold cathode

The grid-free electron gun

Based on the field emission results presented above, the grid-free electron gun with the SWCNTs cold cathode is designed using the 3-D electromagnetic simulation software CST44. The electron emission model is set as the field-induced model, and the field emission is described using a simplified F-N equation:

$$J=a{E^2}\exp ({{ - b} \mathord{\left/ {\vphantom {{ - b} E}} \right. \kern-0pt} E})$$
(3)

where a is the field emission linear factor, measured in A/V2, and b is the exponential factor, measured in V/m. For the SWCNTs cathode, a is calculated as 2.04 × 10−8 A/V2 and b as 6.21 × 106V/m based on the above experimental data. Considering the imperfections in the cathode surface, the emission angle is set as 25° in the simulation45.

The schematic diagram of the proposed grid-free electron gun with the embedded cathode is shown in Fig. 3a. The SWCNTs cathode emission surface is positioned at z = 0 mm with the radius of 0.1 mm. The positions and apertures of the control electrode, focusing electrode and anode were initially determined through theoretical calculations46 and then optimized via simulation. The design parameters are provided in Table 2. The emission current is controlled by the control electrode, which functions similarly to the anode in the field emission experiment. The beam focusing performance is optimized by adjusting the structure and applied potential of the focusing electrode to create an appropriate focusing electrostatic lens.

Table 2 Structural and electrical parameters of the cold cathode electron gun.
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Typically, cold cathodes have emitters (such as CNTs) placed on the surface of the cathode substrate plane. In this work, however, the SWCNTs emitters are embedded into the cathode substrate, with the emission surface flush with the cathode surface. The structures of the embedded and non-embedded cathodes are given in Fig. 3b. In the non-embedded structure, the electron emission plane is raised above the cathode substrate plane, which inevitably increases the divergence angle of the electrons near the edges and aggravates the difficulty of electron beam focusing. In this study, the embedded cold cathode can suppress the increase of the divergence angle of the emitted electron beam, thus enhancing the beam focusing performance.

Fig. 3
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(a) The schematic diagram of the proposed grid-free electron gun with embedded cathode. (b) The structure of the embedded cathode. (c) The structure of the non-embedded cathode.

Figure 4 shows the electric field distribution near the cathode surface for both structures as obtained from the simulation. It is observed that the electric field distribution near the edge of the embedded SWCNTs emitters is nearly parallel to the cathode surface, resulting in the electrons near the edge being emitted at a relatively small divergence angle. This result is consistent with the previous analysis. While the electric field on the embedded cathode surface is obviously lower than that of the non-embedded cathode due to the greatly weakened edge enhancement effect. Nevertheless, the electric field on the embedded cathode surface is more uniform, as shown in Fig. 4c, which is conducive to the laminar flow of the electron beam. We have conducted preliminary qualitative experiments using the enlarged cathode and electron gun, and demonstrated that the embedded cathode structure has better beam focusing performance. In future work, we will continue to promote accurate quantitative experiments.

Fig. 4
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Electric field distribution near the cathode surface of (a) the embedded cathode, (b) the non-embedded cathode. (c) The electric field distribution of the two cathodes.

Figure 5 illustrates the simulated electron trajectories of the cold cathode electron guns with both structures. It is evident that the focusing performance of the embedded cold cathode structure has been significantly improved. The beam radius at the anode outlet is about 0.1 mm, which is approximately 11 times smaller than that of the electron gun with a non-embedded cathode. Besides, the focusing electrode voltage needs to be precisely controlled to better control the electron trajectories. Consequently, the grid-free electron gun with the embedded cathode structure is more suitable for a terahertz TWT and has been adopted in the subsequent design of the terahertz TWT.

Fig. 5
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Simulated electron trajectories of the cold cathode electron guns with the embedded structure (red line) and the non-embedded structure (blue line).

The PPM focusing system

 A PPM focusing system is designed to constrain the shape of the emitted electron beam, as illustrated in Fig. 6. The direction of the arrows in the magnetic rings indicates the polarity direction. The parameters of the PPM focusing structure are detailed in Table 3. The simulation employs both the Magnetostatic Solver and the Particle Tracking Solver. The magnetic rings are made of samarium cobalt magnet, and the pole shoes are composed of iron. The radius of the electron beam tunnel is 0.1 mm.

Table 3 Structural parameters of the PPM focusing system.
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Fig. 6
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The structure diagram of the PPM focusing system.

The peak axial magnetic field (Br) and the periodic magnetic field period (L) are initially selected and optimized through simulation based on the specific SWCNTs cathode electron gun. The final magnetic field period L is determined to be 5 mm. The value of Br is calculated using

$${B_r}=\sqrt 2 {B_b}=\sqrt 2 \frac{{8330}}{{{r_b}}}\frac{{\sqrt {{I_0}} }}{{\sqrt[4]{{{U_0}}}}}$$
(4)

where, Bb is the magnetic induction intensity of the Brillouin current flow, I0 is the electron beam current, U0 is the electron beam voltage, rb is the electron beam radius. Considering the high-frequency defocusing and the anode hole effect, the value of Br is set to 0.6 Tesla (T).

To ensure that the electron beam enters the slow-wave structure (SWS) smoothly, the peak magnetic field intensity of the first magnetic ring (Br1) and the second magnetic ring (Br2) near the electron gun is optimized to 0.4- and 0.9-times of Br, respectively. Figure 7a shows the trajectory of the simulated electron beam with the PPM focusing system under Br = 0.6 T. The electron beam still exhibits significant fluctuation, likely due to the use of the planar cold cathode in this study, whereas Eq. (4) is derived based on the Pierce electron gun with a curved cathode. Although the embedded structure is employed in this study, the focusing performance remains somewhat weaker compared to that of a curved cathode. Figure 7b presents the electron beam trajectory obtained through simulation at different values of Br. It can be seen that when Br = 0.8 T, the magnetic field provides the best confinement of the electron beam, resulting in minimal fluctuation. Figure 7c shows the optimized electron beam envelope and the corresponding distribution of the PPM focusing magnetic field intensity along the central axis when Br is 0.8 T. The electron beam passes through 100% without interception. The beam waist is approximately 0.016 mm (at the position of z = 9.3 mm), and the electron beam is confined to a radius smaller than 0.05 mm with small fluctuation, which can meet the application requirements of some terahertz TWTs.

Fig. 7
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Envelope of electron beam (a) with Br = 0.6 T and the corresponding magnetic field. (b) under different Br. (c) with Br = 0.8 T and the corresponding magnetic field.

Design of a Terahertz folded waveguide SWS based on the SWCNTs cold cathode

The folded waveguide (FW) SWS is chosen for this work due to its characteristics of flat dispersion, wide-band output, low loss, and simple structure, as well as its compatibility with modern mature micro-machining technology. These features make it suitable for high-frequency and small-sized terahertz TWT. In this section, a FW SWS operating at 220 GHz, based on the SWCNTs cold cathode described above, was designed using PIC simulation software.

Figure 8 shows the single-period structure diagram of the designed FW SWS, with key parameters detailed in Table 4. The entire SWS adopts a single-segment structure, which can meet the operational requirements and simplify the processing and assembly of the high-frequency system.

Table 4 Structural parameters of the FW SWS.
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Figure 9 shows the simulated dispersion curve and interaction impedance of the designed FW SWS. The normalized phase velocity varies only slightly across a wide frequency range, with the value of approximately 0.234 at 220 GHz. The interaction impedance is relatively high (> 10 Ω), reaching about 17 Ω at 220 GHz. The relatively flat dispersion characteristic and high interaction impedance facilitate wideband impedance matching and efficient beam-wave interaction.

Fig. 8
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The single-period structure diagram of the FW SWS. (a) The front view. (b) The left view.

Fig. 9
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Simulated dispersion curve and the interaction impedance of the FW SWS.

Figure 10 presents the simulated transmission characteristic curves of the designed FW SWS. The SWS consists of 95 periods, with a total length of 39.9 mm. Considering the loss of metal materials (with the electric conductivity of 2.4 × 107 S/m), the transmission coefficient S21 is greater than − 5 dB over the band of 210 ~ 230 GHz, and the reflection coefficient S11 is less than − 15 dB. These values indicate low reflection and efficient transmission of the electromagnetic signal.

Fig. 10
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Simulated transmission characteristic curves of the FW SWS.

According to the dispersion characteristic, the synchronous voltage is set to 14.7 kV, the current is the same with the experimental result and set to 4 mA. The distribution of the input, output and reflected signals over time at 220 GHz is given in Fig. 11a. The output signal remains stable during the time of 5 ns. The output power is 807 mW with an input power of 70 mW, and the reflection signal is minimal. Figure 11b presents the corresponding Fourier transform spectrum diagram of the output signal. The output spectrum is pure, indicating that no oscillation is generated.

Fig. 11
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(a) Simulated input, reflection, and output signals of the FW terahertz TWT with SWCNTs cold cathode electron source at 220 GHz. (b) Frequency spectrum of the output signal with input power of 70 mW.

Figure 12 shows the energy phase space diagram of the particles. The initial electron-beam energy is 14.7 KeV, with most electrons in the deceleration region having energy less than 14.7 KeV. The simulation result indicates that the decelerated electrons give the energy to the electromagnetic signal during the beam-wave interaction process, thereby amplifying the electromagnetic signal.

Figure 13a presents the variations in output power and gain with frequency when the input power is 70 mW. The 3-dB frequency bandwidth of the output power ranges from 217 to 222.5 GHz. The maximum output power of 856 mW is achieved at 221 GHz, with the corresponding gain of about 11 dB. Figure 13b is the simulated output power and gain versus input power at 220 GHz. At this frequency, the saturated output power is 807 mW with the input power of 70 mW, and the corresponding gain is 10.6 dB.

Fig. 12
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The energy phase space diagram of the particles.

Fig. 13
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(a) Output power and Gain in band of 217–223 GHz. (b) Output power and Gain with different input power at 220 GHz.

Conclusion

A terahertz folded waveguide TWT based on the embedded SWCNTs cold cathode is reported in this work. The improved screen-printing method guarantees the high emission current density and enhanced field emission stability of the SWCNTs cold cathode. The designed grid-free electron gun with the embedded SWCNTs cold cathode can get better focusing electron beam. A simulated G-band TWT with the SWCNTs cold cathode achieves a maximum output power of 856 mW at 221 GHz with the corresponding gain of 11 dB. This work verified that the cold cathode with stable high emission current density and good focusing performance is promising to be applied to the terahertz TWT. While there is still a lot of work need to be done to further promote the application of the SWCNTs cold cathodes in actual terahertz TWT.