Active modulators providing the means to manipulate terahertz (THz) waves are one of the important and desirable components in the applications of THz science [1–4]. Tremendous efforts have been devoted to developing efficient THz modulators based on 2DEG, metamaterials, and phase transition materials or photon-injection schemes [5–15]. However, the reported THz modulators are restricted by limitations in terms of modulation depth (MD)/switching ratio (SR), narrowband response, insertion loss (IL), or processing/configuration complexity [16–23]. The SR refers to the ratio of the maximum transmission amplitude to the minimum transmission amplitude through the device. For example, the metamaterial-enhanced THz modulators can only work in a bandwidth about 0.25 THz due to the intrinsic limited bandwidth resonance property of metamaterial [17]. The semiconductor hybrid structures are usually utilized to broaden the operation bandwidth, such as graphene on silicon (GOS) and MAPbI3 on silicon, but these structures need extra material deposition processes. The GOS semiconductor hybrid structure is commonly used as the electrical tunable THz modulator, while the amplitude MD/SR can only reach about 91.6%/12 in the attenuated total reflectance (ATR) configuration due to the limited tunable range of the graphene’s Fermi level [8]. Setting the incident angle as the Brewster angle can further improve the SR to about 32, but this strategy suffers from the high IL due to the inevitable high Fresnel reflection loss [5]. At the same time, the ATR or Brewster angle configuration also complicates the system’s setup. The optical tunable GOS structures overcome this high IL disadvantage, but these architectures require the assistance of additional high-power optical pumping acting as the major obstacle for their practical applications [12–16]. Thus, high-performance THz modulators working in the simple electrical tunable transmission mode with high MD, broad operation bandwidth, and small IL are still in great demand.

The silicon–silica structure is the most widely used one in the semiconductor industry. However, previous reports claimed that the typical MD of this structure is almost 0 using electrical tuning methods [10,21]. While pumped by continuous wave (CW) laser with a power of 1W/cm2, this structure (SiO2/Si) can only reach around 20% in the THz range [16], making it unsuitable to demonstrate high-performance modulators. Thus, this silicon–silica structure is usually used as the substrate of functional modulator materials other than the modulator itself [5,6]. In this work, a high-performance THz modulator scheme was proposed based on the untapped avalanche breakdown transistor (ABT) effect of the conventional SiO2/Si structure. By gradually increasing the gate voltage Vg of the device to a critical value, the device transits from the usual linear mode to a remarkable reversible avalanche breakdown mode. In the avalanche breakdown mode, the conductance of the devices changes steeply, and increasing the gate current leads to a dramatic attenuation of the incident THz wave in the meanwhile. The maximal transmission-amplitude MD is about 99.9% by gradually increasing from 0.1 to 0.9 A. The MD is slightly dependent on the operation frequency and remains larger than 97% in the concerned frequency range from 0.2 to 1.0 THz. The IL of our proposed THz modulator is around 3 dB, which mostly attributes to the Fresnel reflection loss at the interfaces of our devices. Here, the IL is defined as IL=−20log10(t0), with t0 being the initial transmission amplitude when no voltage is applied. The mechanism of our THz modulator is investigated in detail. The carrier multiplications process in silicon accompanying the avalanche transistor effect of the devices is the main cause of the severe absorption of THz waves. The Drude model is used to theoretically explain the modulation performances of our THz modulator, and it agrees pretty well with experimental data. Finally, we present a comparison between the performances of the proposed THz-ABT modulator. We found the overall performance of the THz-ABT modulator is excellent considering the simple configuration and fabrication of this device.

Figure 1 shows our experimental setup [Fig. 1(a)] and a schematic of our proposed avalanche transistor THz modulator [Fig. 1(b)]. The device simply consists of a 300 μm low-resistivity (ρ=10–15Ω·cm) p-Si substrate with a 58 nm silicon oxide insulator layer on top. As shown in Fig. 1(c), two square metal strips were carefully placed onto one side of silicon as top electrodes, and silicon removed the native oxide layer by soaking it in hydrofluoric acid before plating the bottom electrode (see Appendix A, Fig. 5). Then 58 nm thick silicon dioxide was deposited on the other side of silicon. The average thickness of SiO2 is approximately 58 nm, characterized by cross-sectional scanning electron microscopy as illustrated in Fig. 1(d). The square electrode has a side length of 12 mm and a width of 2 mm, and the area of the uncovered electrode in the middle is 10mm×10mm. TiAu electrodes were deposited on both sides of the device to apply the manipulation voltage. As the gate voltage Vg gradually increases to about 50 V, the current is linearly increasing with small amplitude noted as the linear mode. After that sudden increase of the current and decrease of gate voltage were observed, as indicated by a black dashed arrow in Fig. 1(e). The corresponding conductance is steeply increased, as illustrated in Fig. 1(f). This extraordinary phenomenon means the silicon was entering the reversible avalanche mode [24–28]. The avalanche breakdown of silicon refers to the phenomenon that the current as well as the total power increases exponentially at a critical voltage (see Appendix B, Fig. 6)

In the linear mode, the power supply acts as the constant voltage source and the current of the device also slightly increases with the applied gate voltage. In this mode, the total resistance of the device is quite large mainly contributed by the silicon oxide insulator. As the voltage approaches a critical value of about 50 V, a tunneling effect occurs in the silicon dioxide layer leading to an abrupt decrease of its resistance, and the voltage dropped on the silicon increases dramatically at this situation. As a consequence, p-silicon enters the avalanche breakdown zone. Considering the power supply we used has a protecting value of the total output power, the device transits to the avalanche mode with the gate voltage drastically reduced and the current reaching a balanced value. In this avalanche mode, the power supply acts as a constant current mode. Thus, the current of the device was tuned to electrically manipulate its performance. Next, the current was carefully tuned from the avalanche breakdown point back to about 0.1 A and it is still working at the avalanche mode. Then, the current was gradually tuned up from 0.1 to 0.9 A. The corresponding gate voltage decreases as the current increases.

A home-made THz time-domain spectroscopy (TDS) system was used to measure the transmission spectra of the device under different current Ig in the avalanche mode [Fig. 1(a)]. The incident angle of the linearly polarized THz pulse is set to be 0°. The THz waves were generated via an InGaAs photoconductive antenna (PCA) under bias voltage, which was pumped by fiber laser pulses (central wavelength of 1560 nm, repetition rate of 100 MHz, and pump power of ∼20mW). The size of the focused spot was approximately 2 mm through a 4f system (two lenses with identical focal lengths of 50 mm). In the meantime, THz waves were coherently detected by another PCA with detection power of ∼20mW. The signal of the terahertz receiving antenna was recorded by the lock-in amplifier and transmitted to the computer [7]. The signal-to-noise ratio (SNR) of our THz-TDS system is larger than 1000:1 and the bandwidth of THz-TDS is from 0.2 to 1.0 THz [20]. Our device was located where the terahertz wave was focused to measure the modulation effect (see Appendix C, Fig. 7). This high SNR is significant to obtain the accurate THz signal with small amplitude especially in the situation of large current. Figure 2(a) shows the measured time-domain THz signal of the device under different currents in the avalanche mode. It was observed that the increased current caused significant attenuation of the transmitted THz pulse. As shown in Fig. 2(a), under the current of 0.9 A, the amplitude of the transmitted THz pulse almost disappeared, which indicates the modulation depth of our THz modulator is pretty high. Meanwhile, we also investigated corresponding transmission spectra of our device at the currents of 0.1, 0.3, 0.4, 0.5, and 0.9 A, respectively, as shown by the open markers in Fig. 2(b). At the current of 0.9 A, the transmission spectrum is nearly zero in a wide frequency range. The transmission of our devices is obtained using the formula t(f)=|Es(f)/Er(f)|, where Es(f) and Er(f) are Fourier transformed from the time-domain signal transmitted through the sample and air, respectively. In order to avoid Fabry–Perot oscillations, we keep the first transmitted THz pulse with the help of a window function (see Appendix C, Fig. 8).

Figure 2(c) represents the MD of the avalanche transistor under the current from 0.1 to 0.9 A in the avalanche mode at 0.7 THz. It can be seen that as the current gradually increases, the transmission of the avalanche transistor is decreased. The MD approaches 1 when the current is 0.9 A. Here, the MD and SR are defined as MD=(tg−t0.1A)/t0.1A and SR=t0.1A/tg, respectively, where t0.1A and tg are the transmission under gate current of 0.1 A and Ig at 0.7 THz, respectively. The maximum MD of our avalanche transistor 99.9% (SR of 1000) was achieved when 0.9 A current applied in our experiment. In the meantime, by moving the device so that the THz wave passes through different positions of the device, we find that the MD of the THz wave has not changed. For a comparison, Fig. 2(d) shows the transmission of avalanche transistor under different voltages in the linear mode; it was found that the MD is around 0 for the linear mode. The MD is near 0 in the linear mode, which is due to the fact that conductivity of the transistor is fairly low and the conductivity change is negligible in this mode. We also fabricated a commonly used monolayer graphene field-effect transistor (FET) with the same thickness of p-type silicon and silicon dioxide as the avalanche transistor. We found that the transmission change of the THz-FET modulator in the linear mode is less than 10% considering the limited carrier concentration adjustment of monolayer graphene by applying a biased gate voltage [29]. Therefore, the avalanche transistor shows a strong application prospect as a high-performance THz modulator.

The change trend of MD is consistent with the measured I–V characteristic of the device. As the gate current Ig increases in the avalanche mode, the conductivity and the MD of the devices increase (see Appendix C, Fig. 9), meaning the carrier concentration density in the p-silicon also increases. Thus, the transmission of THz waves is attenuated due to the absorption and the reflection and the MD becomes larger. After it reaches 0.9 A, the gate voltage turns down and the transmission of THz increases with smaller and smaller MD. When the current approaches 0.9 A, a saturation phenomenon of MD is observed [18]. The back and forth tuning of the gate current shows that the performance of the avalanche transistor is reversible. In the meantime, we also found that when changing the direction of the gate voltage, the modulation effect is basically the same. This result implies that the carrier density of the avalanche transistor is only related to the value of the current and is independent of the direction of the gate current.

From the THz-TDS signals, we know that the modulation is not an interface but a bulk effect (see Appendix D, Fig. 10). Thus, the p-silicon of our avalanche transistor should be treated as a bulk, and the transmission of the THz pulse can be simply expressed as |t(f)|=|4n˜(1+n˜)2||e−κωdc|,(1)n˜=n−iκ=ε˜,(2)ε˜=ε∞−σDCiε0ω(1−iωτ),(3)where n˜ and ε˜ are the complex refractive index and the complex permittivity of p-silicon, respectively. ω=2πf is the angular frequency of the THz wave, c is the vacuum light speed, and d=300μm is the thickness of p-silicon. Here, the Drude model was used to describe the complex permittivity ε˜ of p-silicon, where ε∞=11.7 is the constant permittivity at the infinite frequency, σDC is the conductivity of p-silicon at direct current (DC), 1/τ=2π×2THz is the carrier collision frequency, and ε0 is the vacuum permittivity [30,31]. With the above formula, we can fit the transmission spectrum and obtain the parameter σDC under different gate currents (details of the fitting of the transmission spectra can be found in Appendix E, Table 2, Figs. 11 and 12) [32,33]. The experimental and theoretical data agree well with each other, indicating that the behavior of the avalanche transistor can be well explained by the bulk effect of p-silicon. As shown in Fig. 3(a), the real part of permittivity decreases as the gate current becomes larger, which explains the THz signal gradually increasing at the reflection configuration [see Appendix D, Figs. 10(b) and 8(c)]. In the meantime, the imaginary part of permittivity of p-silicon becomes larger and larger, indicating that the absorption is increased as well as deeper and deeper MD of the THz wave. As the imaginary part of the permittivity increases, there is an increasing impedance mismatch with the surrounding air resulting in increased reflection [24]. In the high-THz frequency region, the modulation of the device will gradually decrease as the frequency increases. The device has a high modulation depth of over 90% at 0.2–2.3 THz, which shows excellent potential (see Appendix E, Fig. 13).

In order to further understand the avalanche breaking down process of p-silicon, we also investigate the relationships between the DC conductivity, the carrier density of p-silicon, and the gate current, shown in Fig. 3(c). The relationship between the conductivity and the carrier density is determined by n=σDCm*/τe2, where m*=0.26me is the effective mass of the carrier in p-silicon [30,34]. It can be seen that the conductivity and the carrier density increase with the gate current. These results are consistent with the measured conductivity of the device in the avalanche mode. At the currents of 0.1 and 0.9 A, the carrier’s densities are about 4.14×1014cm−3 and 2.99×1016cm−3, which is still in a reasonable range for p-silicon.

The plasma frequency ωp=σDC/ε0τ has also been calculated, as illustrated in Fig. 3(d) [31]. We found that the plasma frequency is of the same order of the concerned THz range. Thus, strong absorption of the incident THz wave is expected [35], which is essential for a broadband THz modulator. Conversely, when the current decreases, the carriers decrease and result in a lower MD. So the dynamic modulation can be done by changing the gate current.

As analyzed above, in the avalanche mode, the modulation mechanism of the avalanche transistor is using the gate current to adjust the carrier concentration injected into the p-silicon. As more carriers are injected, the total current becomes larger and results in a higher MD of the THz wave. Conversely, when the current decreases, the injected carriers decrease and result in a lower MD. So the dynamic modulation can be done by changing the gate current or the injection of carriers.

In this section, we use the photon-doping method as a straightforward way to inject the carriers [see Appendix F, Figs. 14 and 15]. As illustrated in Fig. 4(a), the dynamic modulation characteristic performance of the THz-ABT modulator was measured at 220 GHz carrier. A square-wave voltage was applied to the acousto-optic modulator to tune the power of the photon-doping laser between 0 and 100 mW. The state of the device is in the avalanche mode with a gate current of 0.3 A. A typical normalized MD of THz transmission at the modulation frequency of 1 kHz is given in Fig. 4(b). Figure 4(c) gives the normalized MD of the THz-ABT when the modulation frequency turns up to 12 kHz. The normalized MD is decreased to about 3 dB at this modulation frequency. The normalized MD magnitude of the THz-ABT at different modulation frequencies was summarized in Fig. 4(d), which indicates a 3 dB operation bandwidth is ∼12kHz.

As shown in Table 1, we compare our THz-ABT modulator with other reported THz modulators based on different materials and different modulation types including the THz-FET, diode, and photon-doping devices. All the devices are based on a similar mechanism by tuning the carrier density to modulate THz waves. The SR of our proposed THz-ABT modulator is more than 5 times larger than the reported works. Meanwhile, our THz-ABT modulators can work in the simple electrical tunable transmission mode with the commonly used silica-on-silicon structure.Table 1.

Comparison of the THz Devices Performance of Amplitude Modulation Depth

Based on the THz-ABT effect, we achieved to switch the THz wave with SR about 1000, which is more than 5 times larger than previous results. The IL has an acceptable value of about 3 dB. In this paper, a new type of THz modulator based on the avalanche breakdown effect of semiconductor has been proven with the ability of achieving the near-perfect MD. It is also worth mentioning that this THz-ABT device can work in the simple transmission mode, which can be applied in vast fields of THz science. The simplicity and convenience of this THz-ABT modulator will undoubtedly attract more and more attention of researchers in the near future.