*3.1. Responsivity*

The responsivity (*R*v) was determined by the output voltage difference Δ*Vout* and the incident power *Pin*. Δ*Vout* was obtained by monitoring output voltages of detectors while THz waves were on and off. *Pin* was calculated by the effective area *Aeff* of the antenna and incident power density *Jin*, which was obtained by the total power of the THz beam and the area of the focused beam. *Rv* and *Aeff* could be expressed as follows [35]:

$$R\_v = \frac{\Delta V\_{out}}{P\_{in}} = \frac{\Delta V\_{out}}{f\_{in} \cdot A\_{eff}} \tag{1}$$

$$A\_{eff} = \frac{G \cdot \lambda^2}{4\pi} \tag{2}$$

where *G* is the gain and *λ* is the EM wavelength in free space.

The block diagram of the output voltage measurement setup at 0.91 THz is shown in Figure 6a. The backward-wave oscillator (BWO) radiated THz waves with an average power of about 125 μW at 0.91 THz. Adjusting the height and position of two parabolic optical mirrors, as the THz beam was reflected by the first parabolic mirror, almost all THz waves were collimated and incident to the parallel second parabolic mirror. Then, after reflection and focusing, a THz beam with a diameter of about 1.15 mm was obtained. Detectors mounted on a three-dimensional stage were positioned at the focus point of the THz beam. A mechanical chopper with a minimum chopping frequency of 2 Hz modulated the THz beam, and a chopper controller modulated the chopper and the lock-in amplifier synchronously. The detector was biased at 2.5 V using a DC voltage source, and the output voltage was measured by a lock-in amplifier. As shown in Figure 6b, DUT 1 achieved the highest responsivity of 32.6 V/W as it resonated at 0.91 THz with a chopping frequency of 2 Hz. The responsivity at 0.91 THz was higher than the responsivity at both sides of 0.91 THz for the following reasons. On the one hand, the EM modeling of the antenna fully considered the design rules and implementation methods of the process in order to ensure that the antenna model was highly consistent with the layout. On the other hand, the circumference of the outer octagonal ring constructed by the metal 9 layer determined the operation frequency, and the processing tolerance of the metal 9 layer was ±0.135 μm. However, even with the maximum processing tolerance, the receiving of 0.91 THz waves was still higher than the receiving of THz waves on both sides of 0.91 THz. Furthermore, the responsivity of DUT 2 was close to zero as there was no significant voltage variation while THz waves were on or off.

**Figure 6.** (**a**) Output voltage measurement setup as detectors operate at 0.91 THz. (**b**) Responsivities.

Figure 7a shows the output voltage measurement setup at 2.58 THz. A quantum cascade laser (QCL) radiated 2.58 THz waves with a peak power of 60 mW and a duty cycle of 4%. The 2.58 THz beam with a diameter of about 500 μm was collimated and focused using two parabolic optical mirrors. The detector was biased at 2.5 V and the output voltage was measured by the SR830 lock-in amplifier. The responsivity as a function of modulation frequency was acquired by modulating the QCL and the amplifier simultaneously using a signal generator. Figure 7b shows the measured responsivities of DUT 1 and DUT 2 versus modulation frequencies. Because the duration of THz waves on detectors increased as the modulation frequency decreased, the output voltage and responsivity of detectors gradually increased until the output was saturated. DUT 1 almost reached saturation at the modulation frequency of 0.5 Hz with a responsivity of 43.2 V/W, while DUT 2 showed responsivities of near zero.

**Figure 7.** (**a**) Output voltage measurement setup as detectors operate at 2.58 THz. (**b**) Responsivities.

Figure 8a shows the output voltage measurement setup at 4.2 THz. A QCL provided 4.2 THz waves with an average power of about 0.5 mW and a duty cycle of 40%. The THz beam with an average power of about 0.15 mW and a diameter of about 209 μm was incident on the chip because of the strong absorption of 4.2 THz waves. The SR830 lock-in amplifier outputs synchronous modulation signals to the QCL and the output signal of the detector simultaneously. The responsivity as a function of modulation frequency from 0.3 Hz to 3 Hz was obtained from the lock-in amplifier as the detector was biased at 2.5 V. Figure 8b shows the measured responsivities of DUT 1 and DUT 2. DUT 1 almost reached saturation at the modulation frequency of 0.5 Hz with a responsivity of 40 V/W, while DUT 2 showed responsivities of near zero.

**Figure 8.** (**a**) Output voltage measurement setup as detectors operate at 4.2 THz. (**b**) Responsivities.
