## 2 Si CMOS Detector  
The planar antenna-coupled THz detector based on Si CMOS FET was used for experiments. The TeraFET employs a single-transistor layout based on the n-MOS transistor with an ultra-low threshold voltage of 445 mV, where the channel length is 100 nm and the width is 1 \(\upmu\)m. The device was fabricated by TSMC (Taiwan, a foundry service provided by Europractice) using a 90 nm technological node. The TeraFET design was optimized using an in-house developed physics-based circuit model [20; 21]. The antenna is implemented in the metal-dielectric stack of the CMOS's back-end. Each antenna leaf consists of two almost identical shapes, arranged in two metal layers (see Figure 1b). The circuit of connections between the antenna leaves and transistor contacts ensures asymmetric power coupling into the channel from the source side only, which is an essential condition of plasma-wave rectification [26; 27; 28; 29]. Additionally, it ensures the necessary electrical isolation between the gate terminal for applying DC bias and the readout of the rectified signal from the drain terminal. More details on the design can be found in [21]. Antenna _EM_ analysis results have shown that the bigger part of the _EM_ energy is emitted into the semiconductor substrate side rather than into the air. Therefore, an additional Si substrate lens is required for efficient coupling between an antenna and THz radiation, which is directed from the substrate side. For the characterizations of detector response, we employed a tunable multiplier-based source fabricated by Virginia Diodes Inc. (VDI) as well as photomixer sources fabricated by Toptica GmbH (more details on the measurement technique can be found in [21; 30]). The VDI source can be tuned over a frequency range from 500 to 750 GHz, and Toptica's--from 50 GHz to 2.2 THz. Our experimental setup for homodyne detection includes two InGaAs photodiodes with a bow-tie photoconductive antenna (labeled TX). The photomixers include hyperhemispherical Si lenses and have slight differences in output characteristics. More information on specific properties of TX modules can be found in [31]. For the calibration of available THz power, we used a large aperture detector from Thomas Keating Ltd. In addition, we performed comparisons of detector broadband performance with a Golay cell detector purchased from Tydex Optics Inc. and a calibrated pyroelectric detector. The last one was manufactured by SLT Sensor GmbH [32], and it has a 20 mmaperture and 42.3 V/W sensitivity (its calibration was provided in combination with a preamplifier by the manufacturer at 1.4 THz). Figure 2a provides the detector's optical voltage responsivity \(\Re_{\text{V}}\) (V/W) as a function of the gate voltage \(V_{\text{g}}\). The responsivity is calculated from the measured peak-to-peak value of voltage response \(V_{\text{det}}\) and the power in the beam:  
\[\Re_{\text{V}}=\frac{V_{\text{det}}}{P_{\text{THz}}}, \tag{1}\]  
where \(P_{\text{THz}}\) is a peak-to-peak value of an incident THz power, which in our measurements with the VDI multiplier source was 10 uW at 609 GHz. For direct power response measurements, we used an 880 Hz chopping frequency. The maximal modulation frequency of TeraFET can reach as high as a typical cut-off frequency \(f_{\text{T}}\approx\) 100 GHz; however, the speed of response of the practical system is limited by the read-out circuitry, which for our devices was about 4 MHz. The knowledge of optical responsivity, as well as the resistance of the channel with the concomitant spectral density of voltage fluctuations, enables estimation of the NEP for these detectors, which is presented in Figure 2a. The NEP of the detector can be derived as:  
\[NEP=\frac{\sqrt{4k_{\text{B}}TR_{\text{DC}}\Delta f}}{\Re_{\text{V}}}, \tag{2}\]  
where \(k_{\text{B}}\) is the Boltzmann's constant, \(T\) is the room temperature, \(R_{\text{DC}}\) is the DC resistance of the transistor's channel and \(\Delta f\) is the equivalent noise bandwidth.