1. Introduction

Terahertz technology has shown its transformative influence in many applications, including ultrafast wireless communications, label-free sensing, and biomedical imaging [1–9]. In particular, broadband THz imaging technology can not only be used to visualize the profile of targeted samples, but also provide spectroscopic information. The THz imaging technique is distinct from that using visible or infrared frequencies, where focal-plane-array-based cameras are utilized, because large-scale THz detector arrays are not available. Compressive sensing provides a new approach to imaging by using sub-Nyquist sampling with a single detector and spatial light modulators (SLMs) [10,11], which has the potential for real-time THz imaging [12,13]. The major challenge then lies in the design of THz SLMs. In a THz compressive sensing imaging system, the SLM modulates a THz light beam that propagates through a sample and onto a single detector. The measured signal is correlated with the spatial pattern and the sample’s spatial transmission function; hence the THz image of a sample can be reconstructed by measuring the THz signal using various mask patterns through a single detector. Mechanical [14,15], optical [16–19], and electrical [12,20,21] methods have all been utilized to spatially modulate THz signals. Among them, the mechanical method is broadband but low frequency; the optical method used to be power-consuming and bulky, but the newly reported waveguide structure [22] and hybrid metal–silicon metasurface [23] have demonstrated improved efficiency and compactness; and the electrical method is compact and high frequency, but normally narrowband [12]. The electrical THz modulators are mostly based on the resonant effect of metamaterials, which limits their operational bandwidth, and a novel mechanism would be required to widen it. A graphene-based THz modulator has been reported to achieve broadband modulation, but only with a depth of ∼17% [24], which was later improved to ∼77% in the frequency range of 0.2 to 1.4 THz using total internal reflection (TIR) geometry [25]. Further improvement of the modulation depth of broadband graphene-based devices is very challenging due to the quality of the graphene and insulation layers. Moreover, the fragility and nonuniformity of graphene-based devices limits their wide application [26,27]. GaAs-based semiconductor devices are an option due to their sophisticated fabrication and robust construction [28–30]. However, previously reported metamaterial-based GaAs devices can only perform narrow bandwidth operations. A GaAs Schottky diode device with integrated microslits operating in transmission mode by stacking two devices back-to-back was reported to achieve ∼75% modulation depth in the frequency range of 0.4 to 1.4 THz, but at a cost of 25 dB insertion loss [31].

Here, we designed, fabricated, and demonstrated an efficient, broadband, and high frequency THz modulator, which exploited a GaAs Schottky diode with integrated microslits using TIR geometry. In TIR, the evanescent wave interacts with the free carriers in the n-GaAs layer and is attenuated. The attenuation of the evanescent wave is controlled by a reverse voltage between the Schottky and Ohmic contacts, which manipulates the free carrier concentration in the slits. Our design achieved an average modulation depth of ∼70% in the frequency range of 0.2 to 1.2 THz and reached a maximum of 90% over 0.25 to 0.4 THz. By encapsulating the GaAs device in a non-conductive material, liquid paraffin, the modulation depth was further improved to ∼100% in the frequency range of 0.4 to 0.6 THz. Moreover, the insertion loss from the active layer was less than 8 dB. Even if we considered reflection loss from the prism surface, the total insertion loss was still less than 13 dB. The 3 dB bandwidth operational frequency was ∼160 kHz. The modulation depth and operational bandwidth of our system is superior to that of existing graphene-based and metamaterial-based THz modulators.

2. Theory and design

This study used a GaAs Schottky diode structure [illustrated in Fig. 1(a)] comprised of an n-GaAs layer and a periodic array of subwavelength metal microslits. By applying a reverse bias voltage between the Schottky and “U”-shaped Ohmic contacts [Fig. 1(b)], sheet conductivity could be manipulated by depleting the free carriers around the microslits to modulate the THz signal. For transmission, a GaAs Schottky device with integrated metal microslits produces ∼40% modulation depth [31]. To improve the modulation depth of the THz modulator, one possible approach is to increase the interaction length of the THz wave and conductive material. Thus, stacking two devices to form a back-to-back device achieves ∼75% modulation depth but introduces a 25 dB insertion loss [31]. One approach to increasing interaction length while reducing insertion loss could be to exploit TIR geometry. The evanescent wave propagates along the interface for a short distance, called the Goos–Hänchen shift [32], which can improve modulation depth while maintaining bandwidth [25,33,34]. The periodic subwavelength microslits can further improve the performance of a TIR-configured modulator due to its non-resonant electric field enhancement effect [25,35,36]. In this study, TIR geometry was used to improve the performance of a GaAs Schottky modulator with integrated metal microslits [Fig. 1(c)]. The substrate material is intrinsic GaAs (n₁ = n_GaAs = 3.58), and the overlying material is air (n₂ = n_air = 1) or liquid paraffin (n₂ = n_{liquid paraffin} = 1.48). The critical angle of the air/GaAs interface is 16.2°, and the critical angle of the liquid paraffin interface is 24.4°. The incident angle is set to θ_i = 28.5°, which is a result of the particular geometry of our system and supercritical for both cases. The electric field enhancement factor η is defined as η = P/g, where P is the spatial period and g the gap width of the metal microslits. Four enhancement factors, η = 2, 5, 7, 10, were chosen for testing. The equation to calculate the reflection coefficient of the conductive layer with integrated metal microslits using TIR geometry has been described previously [25]. In the equation, reflection intensity is related to incident angle, refractive index of the dense and less dense materials, and sheet conductivity. The theoretical results show [Fig. 1(d)] that when the sheet conductivity of the n-GaAs layer increases from 0 to 10 mS, reflection intensity exhibits a rapid decrease followed by a more gradual increase. With a larger enhancement factor η, the sheet conductivity required to reach a minimum reflection intensity is lower. For example, when η = 2, the required sheet conductivity to achieve the minimum is around 5 mS, but when η = 10, the required sheet conductivity to achieve the minimum is less than 1 mS. Another parameter that influences reflection intensity is encapsulation. When the model was encapsulated in liquid paraffin (η = 5, green dashed line), the refractive index of the less dense material was changed from 1 (air) to 1.48 (liquid paraffin). Encapsulation reduces the minimum in calculated reflection intensity. In the theoretical model, when the sheet conductivity changes from 3.5 to 5 mS, the reflected intensities corresponding to the various enhancement factors exhibit different trends. The reflected intensities at these two values of sheet conductivity are highlighted by hollow circular dots in Fig. 1(d). For η = 2, reflection intensity at 3.5 mS is higher than that at 5 mS; while for η = 5, 7, and 10, reflection intensities exhibit the opposite trend. This phenomenon can be explained as follows: when sheet conductivity is zero, reflection intensity is unit; when sheet conductivity is ∞, reflection intensity is also unit; when sheet conductivity is between 0 and ∞, reflection intensity is less than unit due to absorbance within the conductive layer; at a particular value of sheet conductivity, reflection intensity reaches a minimum; at lower conductivity, reflection intensity decreases due to greater absorbance in the conductive layer; at higher conductivity, reflection intensity increases due to the conductive layer being more reflective. Therefore, when sheet conductivity changes from 3.5 to 5 mS, absorbance is dominant for η = 2; while the reflection is dominant for η = 5, 7, and 10.

 

Fig. 1. (a) Schematic of GaAs Schottky diode structure with TIR geometry. An n-doped GaAs layer was grown on the semi-insulating GaAs (SI-GaAs) substrate. The area of metal microslits consists of a Schottky contact surrounded by a “U” shape Ohmic contact. The GaAs Schottky device is placed on a prism; the incident THz light in s-polarization (out-of-plane) is reflected off the surface of the metal microslits. (b) Photograph of a GaAs Schottky diode with integrated microslits on a silicon prism surface. A reverse voltage was applied to the Schottky and Ohmic contact by a pair of probes. (c) Schematic diagram of the experimental setup of THz measurements using TIR geometry. The s-polarized incident THz light has a 30° angle to the normal and is refracted through the GaAs substrate. The encapsulation material on the surface of GaAs Schottky diode could be air or liquid paraffin. (d) Theoretical calculations of reflection intensity as a function of optical sheet conductivity and enhancement factor (η = P/g). P represents the spatial period of the microslits, and g represents the gap width. The refractive index of the dense material (GaAs) was 3.58 and the less dense material was 1 (air) or 1.48 (liquid paraffin). The angle from the dense to less dense material was set to 28.5° (this angle was a result of the particular geometry of our system). The red, green, orange, and purple solid lines represent reflection intensity with enhancement factors of 2, 5, 7, and 10, respectively. The effect of metal microslits of η = 5 with encapsulation material (liquid paraffin) is shown by the green dashed line. The yellow rectangle represents an example of a tunable range of sheet conductivity.

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3. Experiment

An n-GaAs layer with thickness of 0.62 µm and free carrier density of 2×10¹⁷ cm⁻³ was grown on an intrinsic GaAs substrate by molecular beam epitaxy (MBE). The frequency-dependent optical sheet conductivity of the n-GaAs layer was measured by a THz time-domain spectroscopy system (TERA-K15, Menlo Systems) and is shown in supplementary material Fig. S1. The fabrication details of the Schottky and Ohmic contacts have been described previously [31]. The GaAs device is placed on the top surface of a high-resistivity silicon prism [isosceles triangle, each base angle is 30°, Fig. 1(c)]. To securely attach the GaAs substrate to the prism, two electrical probes were used, which also supplied the reverse voltage. High-resistivity silicon is a widely used material for THz prisms, but to minimize reflection loss from the silicon prism and GaAs substrate due to the refractive index mismatch (n_si ≈ 3.42, n_GaAs ≈ 3.58), a GaAs prism could be used in the future. The THz light had a 30° incident angle to the normal, which refracted into the GaAs substrate and yielded a 28.5° incident angle at the TIR interface. A schematic diagram of the TIR experiment is shown in Fig. 1(c). In this study, the width of the microslit gap was fixed at 2 µm with periods of 4 µm, 10 µm, 14 µm, and 20 µm. They are abbreviated as devices 2-4, 2-10, 2-14, and 2-20, respectively, with corresponding enhancement factors of 2, 5, 7, and 10. The 2 µm slit width is limited by our stand UV photolithography technique. In the future, with more advanced technique, such as DUV (deep ultraviolet) or electron beam lithography, finer slits can be achieved, which will provide wider operational bandwidth [35].

4. Results and discussion

The reverse voltage was set below 5 V, which was close to the breakdown voltage of our Schottky diode, as described in our previous experimental study [31]. Figures 2(a)–2(d) show the evolution of the time-domain waveforms as the voltages were swept from 0 to 5 V. Device 2-4 had a maximum electric field amplitude of 5 V and maximum attenuated value of 0 V; devices 2-10, 2-14, and 2-20 all had maximum reflected electric field amplitudes of 0 V and maximum attenuated values of 5 V. The experimental results were consistent with the above theoretical predictions. For all four devices, the time-domain waveforms were gradually modulated by the applied voltages, which indicated that the THz signal could be modulated electrically. The time-domain signal of the four devices was windowed to eliminate multiple reflections from the GaAs substrate and silicon prism. Fast Fourier transforms (FFT) were used to calculate the frequency-domain signal from the time-domain signal. The frequency-domain signal of the four devices is shown in Supplement 1, Fig. S2. Frequency-domain modulation depth is calculated using the following equation: $({1 - E_V^2/E_{max}^2} )\times 100{\%}$, where E_v denotes the frequency-dependent amplitude of the reflected THz wave with a reverse bias from 0 V to 5 V, and E_max denotes the maximum amplitude of the reflected THz wave. For example, E_max was the electric field amplitude at 5 V in device 2-4, while E_max was the electric field amplitude at 0 V in device 2-20.

 

Fig. 2. (a)–(d) Reflected THz waveforms of devices 2-4, 2-10, 2-14, and 2-20 for six reverse voltages between 0 and 5 V. The time-domain signals of the different devices are horizontally shifted along the optical delay axes for clarity.

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Figure 3(a) shows the modulation depth of the four devices in the frequency range of 0.2 to 1.2 THz, which was limited by the signal-to-noise ratio of our system (as shown in Supplement 1, Fig. S2). Device 2-4 (η = 2) had a modulation depth of less than ∼40%, which was the lowest among the four devices. Device 2-10 (η = 5) had the highest modulation depth in that frequency range among the four devices, which reached ∼90% for frequencies of 0.25 to 0.4 THz. The modulation depth then decreased as the enhancement factor increased from 7 (device 2-14) to 10 (device 2-20). This can be explained by our theoretical model, as shown in Fig. 1(d). Given that the optical sheet conductivity of our n-GaAs layer at f = 0.5 THz was around 5 mS, and assuming that sheet conductivity can be tuned between 3.5 and 5 mS, theoretical modulation depths can be calculated from the difference of reflected intensities [highlighted by the hollow dots in Fig. 1(d)]. For devices 2-4, 2-10, 2-14, and 2-20, the corresponding theoretical modulation depths were ∼22%, ∼43%, ∼33%, and ∼25%, respectively. In the theoretical model, device 2-10 had the highest modulation depth, which was lower in 2-4 and also decreased with further increases in enhancement factor. These experimental results are generally consistent with the theoretical predictions, although there are slight mismatches of modulation depth with theoretical values that can be explained by the difficulty in establishing accurate sheet conductivity for the Schottky diodes. As shown in the theoretical results of Fig. 1(d), by encapsulating the metal microslits in liquid paraffin, the refractive index of the less dense material is increased. Thus, reflection intensity can be further lowered and modulation depth improved. There are three reasons for using liquid paraffin as the encapsulating material: (1) it is non-conductive, thus electrically isolating the Schottky and Ohmic contacts; (2) liquid paraffin can flow and completely cover the area of microslits, reducing the risk of formation of air bubbles that can lead to multiple reflections in the package; and (3) liquid paraffin has low absorbance and achromatic refractive index (n ≈ 1.48) in the THz range [37]. In the future, for easy fabrication and assembly, polymer material can be used to replace liquid paraffin for encapsulation. The modulation depth of encapsulated device 2-10 is shown in Fig. 3(b). Its overall modulation depth with liquid paraffin was higher than that without encapsulating material. In the frequency range of 0.4 to 0.6 THz, the modulation depth was close to 100%. The insets of Fig. 3(b) show photos of the encapsulated device. The thickness of the paraffin layer was around 2 mm, which was larger than the penetration depth of the exponentially decaying THz evanescent wave in TIR. The decrease in modulation depth observed below 0.4 THz for the encapsulated device may have been due to the frequency-dependent incident angle in the THz time-domain system, where the low frequency component may have had a subcritical incident angle compared with the critical angle of the liquid paraffin/GaAs model (θ_critical = 24.4°).

 

Fig. 3. (a) Modulation depths of devices 2-4, 2-10, 2-14, and 2-20 in the frequency range of 0.2 to 1.2 THz without encapsulating material. (b) The green dashed line represents the modulation depth of device 2-10 encapsulated in liquid paraffin; the green solid line represents the modulation depth of the device without liquid paraffin. The insets show photos of a GaAs Schottky diode with liquid paraffin on the upper surface.

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Insertion loss is an important parameter of a THz modulator, with some metamaterial-based designs achieving deep modulation at the cost of extremely high insertion loss, such as 30 dB [38,39]. A Brewster-angle-based broadband THz modulator achieves deep modulation by manipulating the weakly reflected THz signal, thus introducing a 15 dB insertion loss [40]. In this study, the metal microslits and TIR geometry functioned in a non-resonant way, which in theory avoids high insertion loss. The insertion losses in this study mainly arose from three sources: (1) the silicon prism; (2) refractive index mismatch that introduced reflection loss at the silicon prism and GaAs substrate; and (3) absorbance by the undepleted free carriers in the n-GaAs layer. Experimentally, the reflected intensity of a metal plate was taken as the reference to calculate the insertion loss produced by introduction of different optical components (the schematic diagram can refer to the supplementary document). The insertion loss of the bare silicon prism without a sample was around 5 dB for f < 0.6 THz [ Fig. 4(a)]. The insertion loss in our experimental results increased greatly for f > 0.6 THz, which was due to a rapid decrease in the signal-to-noise ratio of our system in the high frequency range. By placing the 2-10 device on the silicon prism interface without a reverse voltage, the insertion loss was around 13 dB. Thus, the insertion loss introduced by placing the device is less than 8 dB. The green line in Fig. 4(a) shows the insertion loss of device 2-10 with liquid paraffin encapsulation, which was similar to that without liquid paraffin. These experimental results show that TIR geometry introduces little extra insertion loss beyond a small amount at high frequencies that can be explained by the slight absorbance of liquid paraffin at those frequencies [37]. The insertion losses of our design can be reduced by (1) manufacturing broadband anti-reflection structures, such as pyramid structures [41,42], on the air/prism interfaces, (2) using refractive index matching material for the prism, such as intrinsic GaAs, and (3) exploiting finer slits to fully deplete free carriers in the gaps to reduce sheet conductivity close to 0, thus reflected intensity can be close to unit, as shown in Fig. 1(d). By using these three approaches, the insertion loss of our design could theoretically be eliminated. By using these two approaches, the insertion loss of our design could be less than 8 dB.

 

Fig. 4. (a) The relative reflected intensity of the silicon prism, device 2-10, and device 2-10 with liquid paraffin encapsulation using TIR geometry compared with the reflected intensity with a metal plate. (b) Normalized modulation depth as a function of frequency and fitted curves of device 2-10 (asterisks and red solid line). The black dashed lines highlight the 3 dB-down bandwidth modulation frequency.

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Another important parameter of THz modulators is operational frequency. Ion-gel-gated graphene devices have achieved deep modulation depths but operate at low modulation frequencies [43,44]; the large-area graphene in a Brewster-angle device also limited the operational frequency to ∼10 kHz [40]. The modulation frequency in our device is constrained by the GaAs Schottky diode, for which the high mobility of free carriers enables high-frequency modulation. By measuring operational frequency in the transmission geometry, modulation frequency using TIR can be estimated. Experimental procedures for measuring operational frequency has been described previously [31]. The 3 dB modulation frequency of the 2-10 device was ∼160 kHz (Supplement 1, Fig. S3). By optimizing the parameters of the GaAs Schottky diode, such as the size of the area of microslits, modulation frequency potentially could be increased into the MHz range [45].

5. Conclusion

In this work, we proposed a broadband electrical THz modulator based on a GaAs Schottky diode with integrated metal microslits in a TIR geometry. By applying non-resonant electric field enhancement of the TIR evanescent wave by the metal microslits, modulation performance was greatly improved. The liquid paraffin encapsulated GaAs Schottky diode with a microslit width of 2 µm and spatial period of 10 µm yielded approximately 100% modulation depth over 0.4 to 0.6 THz. The insertion loss of the device was around 13 dB, which could be reduced to less than 8 dB by optimizing the composition and surface of the prism. The 3 dB modulation frequency was as high as ∼160 kHz, which could be improved by optimizing the layout of the metal microslits. Our first-generation device outperformed existing electrical THz broadband modulators in terms of modulation depth and insertion loss, and it also outperformed metamaterial-based THz electrical modulators in terms of operational bandwidth. By extending the single modulator to a modulator array to spatially modulate a THz beam, our design could be used in conjunction with single-element detectors for compressive sensing imaging and ultimately for broad-bandwidth real-time THz imaging.