1. Introduction

The terahertz detector is an important part of the terahertz (THz) science and technology [1,2], and the sensitivity of the detector is one of the key factors in the development of THz imaging [3] and wireless communication [4]. Finding ways to improve the coupling efficiency of the device is an important topic in the design and preparation of THz detectors. In optical wave bands, the resonant cavity structures that comprise optical films are commonly used to improve the coupling efficiency of optical detectors because optical films with nanometer-scaled thickness are very easy to prepare [5–8]. However, in THz bands, preparing a resonant cavity by conventional means is difficult to conduct when preparing multilayer films given their relatively longer wavelengths. The wavelength of the incident THz radiation is equal to or longer than the thickness of the THz detector substrate, and thus, an obvious interference effect occurs on the upper and lower surfaces of the substrate. This substrate Fabry-Pérot (FP) cavity causes an interference effect that significantly impacts the coupling efficiency of incident THz waves. The FP cavity provides strong light–matter interaction [9], and is used as a filter [10], metamaterial absorber [11], emitter [12], spectrometer [13], and plasmon-polariton [14] optoelectronic integrated circuit [15] in the THz region.

Following the above merits, more and more attention has been paid to the substrate FP cavity effect and antenna-coupled THz detectors based on this effect, given that this structure can enhance detector response due to the electric field strengthened by interference [16–20]. Meanwhile, it is very useful in large-scale array devices for the resonant frequency can be achieved by changing the thickness of the substrate [21–23]. However, it is not clear at the moment whether the planar antenna and substrate effects will have undesirable impacts on the device. Although the effect of substrate thickness on the gain-receiving antenna printed on the substrate was studied extensively for the millimeter wave regions [24–27], the theoretical results are very complicated and obscure. Coquillat et al. [16] conducted a detailed study of single-field effect transistor (FET) detectors integrated with bowtie antenna and substrates of varying thickness. Although a strong dependence of the responsivity on Si substrate thickness was revealed, the relationship between substrate cavity effect and detector responsivity was unconfirmed. Zhang et al. [19] recently analyzed the substrate effect on antenna-coupled FET detectors by adopting the waveguide theory, but experiment results were lacking.

To solve the above problems from literature, we propose a simple method based on the interference theory of the FP cavity to analyze the influence of substrate thickness on antenna-coupled Nb₅N₆ microbolometers. Moreover, we experimentally measure the optical voltage responsivity of the Nb₅N₆ microbolometer THz detector with different substrate thicknesses in the range of 0.16–0.36 THz. The optical voltage responsivity of the Nb₅N₆ microbolometer with different substrate cavity lengths are measured and analyzed by adopting interference theory, and the substrate thickness dependence of the detector is investigated at 0.2, 0.24, 0.3, and 0.35 THz respectively. A variable length of the FP cavity is constituted by simply placing a moveable metallic planar mirror at the backside of the Si substrate. The incident THz radiation is effectively manipulated by changing the substrate-mirror distance to modulate the phase relation between the reflect wave and the incident electronic wave in the Nb₅N₆ microbolometer. The distinct radiation control is observed, and the experiments are explained by numerically analyzing the responsivity dynamics that highlights the role of FP cavity during the radiation process. All of the results discussed here can be extended to a broad range of frequency and other type of THz detectors, such as FET [28] and Schottky barrier diode (SBD) [29].

2. Dipole antenna-coupled microbolometer with different substrate FP cavity thicknesses

Figure 1(a) shows an antenna-coupled Nb₅N₆ microbolometer on a Si substrate. Due to the wave reflections on the interfaces, the substrate acts as a cavity, resulting a dependence of the field intensity at the detector on the substrate thickness L. With carefully tuning L to form a maximum of electric filed at the detector surface, the response of the Nb₅N₆ microbolometer can be maximized. Considering the vertical incident of the electromagnetic wave, the optimal thickness of the substrate can be obtained by the following formula [30]:

 

Fig. 1 (a) Schematic diagram of an antenna-coupled Nb₅N₆ microbolometer with substrate cavity length of L. (b) Optical microscopy image of the Nb₅N₆ microbolometer THz detector.

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The dipole antenna-coupled Nb₅N₆ microbolometer with an air-bridge structure was fabricated on the highly resistive (ρ > 1000 Ω·cm) Si substrate with 200 nm SiO₂ by thermal oxidation. The thickness of the Si substrate is 720 μm. The other geometric parameters of the microbolometer and the fabrication process were consistent with those in the experiments presented in [31,32].

The optical microscopy image of the Nb₅N₆ microbolometer THz detector is shown in Fig. 1(b). The wavelength of the incident THz radiation was roughly equivalent to the thickness of the substrate of the THz detector, and the resonant cavity was formed by depositing a gold film at the backside of the substrate. The Nb₅N₆ microbolometer with different cavity lengths was obtained by grinding the substrate to 720, 670, 580, 440, 370, to 300 μm, and then the gold film was deposited onto the polished surface that was used as the ground plane.

The voltage response of the microbolometer detector was proportional to the electrical intensity at the local position of the Nb₅N₆ micro-bridge. The schematic of the setup used to measure the voltage responsivity is the same as in [32]. THz source is provided by the multipliers from Virginia Diodes, Inc., Charlottesville [33] that multiplies a low-frequency signal to THz frequency range. The output power of THz source is about 0.3 mW, which is varied with signal frequencies. It was modulated using a 4 kHz TTL signal. The radiation is focused to yield the largest possible signal from the detector by two off-axis parabolic mirrors. For alignment procedure, a laser beam was used for rough adjustment, and then the microbolometer was moved until its response voltage reaches the maximum value. The voltage responses of the microbolometers are read out by a lock-in amplifier. The optical responsivity (R_O) was directly extracted from the measured voltage ΔV by using the relationship$R_O=\Delta V/P_{in}$, where P_in is the total radiation power focused by the off-axis parabolic lens. In the formula, the whole power incident on the lens effectively couples to the microbolometer. It is difficult to measure the absolute voltage responsivity of the devices, here we use the optical responsivity ($R_O$) to illustrate the impact of the substrate.

The voltage response of the detector with different substrate thicknesses were initially investigated in fixed frequency. Figure 2(a) shows the substrate thickness dependence of the voltage response for the microbolometer at 0.2 THz. The circles indicate experimental values for the microbolometer on the substrate with different thicknesses. The voltage response of the detector varied periodically with the maximum value much larger than the minimum value (i.e., nearly zero). This phenomenon can be explained by electric field wherein the detector is located, the intensity of which can be calculated by the finite difference time domain method (FDTD). To simplify the simulation mode, the planar dipole antenna was not considered in the simulation. The calculated intensity of the electric field is illustrated by the blue solid lines in Fig. 2. The thickness of the substrate when the electric field reached the maximum value and the number of peaks was obtained through Formula (1). The measured results agreed well with simulation results. As shown in Fig. 2(a), a substrate whose thickness is an odd integer in the multiple of ${\lambda }_g/4$ corresponds to an electric field that is in the maximum (i.e., maximum voltage response of the microbolometer), whereas the voltage response of the detector is nearly zero when the thickness is an even integer in the multiple of ${\lambda }_g/4$ Hence, to obtain the maximum response, the substrate thickness of the antenna-coupled detector should be set to an odd integer in the multiple of ${\lambda }_g/4$. To further verify the rule, the substrate thickness dependence of the voltage response of the microbolometer at 0.24, 0.3, and 0.35 THz were also investigated, the results of which are shown in Figs. 2(b), 2(c), and 2(d), respectively. The measured results roughly agreed with the simulated results. The number of peaks and troughs increased with the frequency. And the value measured for substrate thickness 370 μm in subfigure (a) f = 0.2 THz and (b) f = 0.24, deviates from the model. It may be caused by two reasons: one is the deviated thickness of the substrate caused by sandpaper grinding, the other is the influence of the planar dipole antenna is not considered in the simulation model.

 

Fig. 2 Fixed frequency of the incident THz signal. Device voltage response with different substrate cavity thicknesses: dots represent the measured response voltages of the detector with different substrate device cavity lengths while blue lines represent the simulation results of electric field intensity on the square device with different thicknesses when incident THz frequency is (a) f = 0.2 THz, (b) f = 0.24 THz, (c) f = 0.3 THz, and (d) f = 0.35 THz.

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We also measured the optical responses of the detector in the range of 0.16–0.36 THz with cavity lengths of 720, 580, 440, and 300 μm. The results are depicted by the dotted lines and the calculated intensity of the electric field is represented by the blue solid lines in Fig. 3. The optical responses of the detector with different cavity lengths fluctuated periodically with interval frequency equal to $2f_{\text{0}}$,which are given by Formula (2). The number of peaks and troughs increased with substrate cavity length. In the figure, the curve of the calculated electric field is in good agreement with the curve of the voltage response of the detector. The calculated number and the location of crests and troughs were similar to those of the voltage response of the device. Noticeably, in subfigures L = 440 μm and L = 580 μm, the off resonance enhancements are observed at approximately 0.275 THz, deviates from the simulation model. There are three factors that are not well controlled, which may lead to such measurement results. One is the power measurement error, the other is the uneven surface of the substrate caused by sandpaper grinding, and the third is the absence of the dipole plane antenna in the simulation model. Furthermore, compared with the voltage responses of the detectors with different cavity lengths in Fig. 3, the substrate cavity effect was a major factor in the coupling efficiency of the detector. The dipole planar antenna exhibited lesser effect on the response value of the detector compared with the substrate cavity. Therefore, to derive a resonance-enhanced THz detector at a particular frequency, a certain substrate thickness is initially selected to enhance the electric field on the device, then the THz planar antenna is designed. The theories and methods presented here can also be applied to other types of THz detectors, such as FET.

 

Fig. 3 Voltage response of the Nb₅N₆ microbolometer THz detector with different incident frequencies when the substrate cavity length is fixed. Dots represent relative voltage responses of the device while blue lines represent the simulation results of the electric field intensity at the device location with substrate thickness of (a) L = 300 μm, (b) L = 440 μm, (c) L = 580 μm, and (d) L = 720 μm.

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3. Substrate FP cavity turning by a movable ground plane

Changing the substrate thickness may not always be applicable for device fabrication, especially for high-frequency application, considering the mechanical stability of the wafer. The general physical considerations above suggest that the position of the voltage response peak is influenced by the substrate thickness of the detector.

To exploit the potential of this feature in translating the voltage response peak and the resonant frequency along the frequency axis, an asymmetric coupled FP cavity was constructed by simply placing a movable copper (Cu) plate at the backside of the Si substrate, and this setup was used as a metallic planar mirror with an adjustable air gap. The structure essentially worked as a coupled FP cavity. The cavity effects from the Si substrate and the air gap between the Cu mirror and the dipole plane antenna were considered. The schematic in Fig. 4(a) shows the structure of the Nb₅N₆ microbolometer THz detector with a movable FP cavity. The separation distance between the Si substrate and the planar mirror was tuned using a micro-transition stage.

 

Fig. 4 (a) Schematic of the asymmetric FP cavity with tunable distance between Si substrate and movable Cu plate, in which L is the substrate thickness and the d is the distance from the metal piece to the backside surface of the device, ∆d is moving distance. Here L = 670 µm, d is about 2.6 mm, and ∆d = 100 µm. (b) Measured optical responsivity of the microbolometer with different mirror distances (dotted line) and calculated electric intensity by FDTD as a simple model (blue line).

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The frequency responses of this structural were measured from 0.27 to 0.32 THz in two different locations. The red and dark dotted line in Fig. 4(b) represent the typical measured optical responsivity of the Nb₅N₆ microbolometer with a substrate-mirror distance of d and d + ∆d, respectively. During the movement of the Cu plate, the voltage response of the structured microbolometer exhibited typical oscillations caused by the movable cavity effect, and when the Cu plate was moved by 100 µm (∆d = 100 μm), the resonant frequency is shifted by about 0.01 THz from 0.295 THz to 0.285 THz. The method of adjusting the air gap allows the device to reliably operate and enhance THz radiation by interference, thereby improving device voltage response. The experimental results were verified by the calculations. The electric intensity calculated by FDTD at which the detector is located is plotted in blue lines in Fig. 4(b). The amplitude of the radiated field was strongly dependent on the change in separation distance d, and the enhancement and inhibition of the THz radiation were due to the FP cavity effect. The findings offered a deep understanding of the measured results. As demonstrated in Fig. 4(b), the calculated electric intensity and the optical responsivity are roughly the same shape. However, a slight discrepancy between the calculation and the experiment was observed, and the difference was attributed to the precise measurements of the micro-transition stage,the influence of the plane antenna and the absorption by the detector was not considered in the simulation model.

4. Conclusion

The FP cavity was introduced to enhance the responsivity of the antenna-coupled microbolometer detector. The theoretical analysis for the voltage responsivity of the THz detector with FP cavity was derived and confirmed experimentally using the microbolometer with different substrate thicknesses. The profile and locus of the radiation enhancement and inhibition agreed well with the on and off resonance FP modes of the analytical calculation, as evidenced by the cavity effect on optical responsivity. For each substrate thickness, the appropriate cavity structures were determined to realize the maximum radiation enhancement or inhibition. These results showed that the FP cavity effectively improved the performance of the microbolometer in the THz wave band, and this technique could also be used for other types of THz detectors, such as FET and SBD. Moreover, the results provided a clear picture of THz radiation dynamics in the cavity, which suggest an effective and simple way of controlling the voltage response resonant frequency of the antenna-coupled THz detector on the basis of the FP effect. The present work also provides a deep understanding of previous studies that analyzed the substrate thickness of THz detectors. In addition, this type of structure has a good prospect in the large array of terahertz devices because of its easy integration and advantage in device packaging.