Homodyne Spectroscopy with Broadband Terahertz Power Detector Based on 90-nm Silicon CMOS Transistor

: Over the last two decades, photomixer-based continuous wave systems developed into versatile and practical tools for terahertz (THz) spectroscopy. The high responsivity to the THz ﬁeld amplitude of photomixer-based systems is predetermined by the homodyne detection principle that allows the system to have high sensitivity. Here, we show that the advantages of homodyne detection can be exploited with broadband power detectors combined with two photomixer sources. For this, we employ a THz detector based on a complementary metal-oxide-semiconductor ﬁeld-effect transistor and a broadband bow-tie antenna (TeraFET). At 500 GHz and an effective noise bandwidth of 1 Hz, the response from one photomixer-based THz source resulted in an about 43 dB signal-to-noise ratio (SNR). We demonstrate that by employing a homodyne detection system by overlaying the radiation from two photomixers, the SNR can reach up to 70 dB at the same frequency with an integration time 100 ms. The improvement in SNR and the spectroscopic evidence for water vapor lines demonstrated up to 2.2 THz allow us to conclude that these detectors can be successfully used in practical continuous wave THz spectrometry systems.


Introduction
In recent decades, the terahertz band of electromagnetic waves (THz) has received much attention. The peculiarities of interaction of electromagnetic radiation with many materials at this frequency band give THz an important place in spectroscopy, as well as imaging applications, e.g., for the investigation of molecular crystals and organic molecules [1], for the detection of the concealed weapons or chemical recognition of explosives at airports [2,3], for the detection of drugs and malignant tumors in medicine [4], as well as for quality control systems in industry [5]. THz spectroscopy is also used to study many-body quantum kinetics [6], to discover the cosmic microwave background radiation and interstellar cloud in astronomy [7], and for art conservation [8]. Therefore, by now, there are many reports related to the application of THz technologies in various fields of science: physics, chemistry, biology, medicine, and telecommunication [9,10].
Over the last two decades, the photomixer-based continuous wave systems developed into versatile and practical THz spectroscopy tools [11]. The high sensitivity of photomixerbased systems comes from their sensitivity to the THz field amplitude, which is predetermined by the inherent homodyne detection principle [12]. Moreover, this technique allows estimating frequency-dependent changes in the optical path, allowing for simultaneous assessment of an absorption and a refractive index, i.e., a complex dielectric function.
Recently the development of photonic THz systems took a path that combines photoswitch-based generation and a fast power detector (zero-biased Schottky diode) [13]. This solution became attractive for applications that prefer fast response, and the spectral discrimination was not of primary interest. Whereas commercially offered systems employ zero-bias Schottky diode detectors, there were reports that demonstrated that TeraFETs could also be used in conjunction with time-domain photonic systems [14,15]. Furthermore, CMOS TeraFETs have been reported to be effectively applied as detectors for photomixergenerated THz frequency combs [16].
The advantages of homodyne detection can also be exploited by utilizing broadband power THz detectors and a photimixer-based THz generation scheme. In the beginning, Schottky diodes were demonstrated as candidates for mixing two THz waves [17]. Recently, a diode of an asymmetrically-shaped bow-tie geometrical form was used for homodynebased imaging [18]. Reported state-of-the-art performance [19][20][21] values prove that field-effect transistors (FET) are becoming strong competitors to other established THz detection technologies. The technological handling, temperature stability, and large-area high-volume integration of FETs are, however, much easier to use, because unlike Schottky diodes, they are part of the mature standard processing technology of microelectronics, which is now projected for novel THz photonic use.
Successful homodyne detection at a single frequency in the THz range with FET was demonstrated several times [22][23][24]. Recently, a homodyne-based phase-sensitive terahertz spectrometer concept that utilizes FET as a detector was proposed [25]. Here, we present experimental evidence supporting this theory. We employ a THz detector based on 90 nm Si CMOS FET and broadband bow-tie antenna (also called TeraFET).

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 µm. 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 multiplierbased 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 mm aperture 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 V (V/W) as a function of the gate voltage V g . The responsivity is calculated from the measured peak-to-peak value of voltage response V det and the power in the beam: where P THz is a peak-to-peak value of an incident THz power, which in our measurements with the VDI multiplier source was 10 µW 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 T ≈ 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: where k B is the Boltzmann's constant, T is the room temperature, R DC is the DC resistance of the transistor's channel and ∆ f is the equivalent noise bandwidth. The dimension of such a defined quantity is given in W/ √ Hz. Later in Section 4, we will present experimental noise measurements that validate the applicability of Equation (2).
The maximum responsivity and NEP values appear at different gate voltages (compare both curves in Figure 2a). This is due to the nonlinear dependency of the DC drain-source resistance R DC on the gate voltage. The maximum voltage response, and corresponding responsivity, were at the gate voltage bias 180 mV, and the minimum NEP was at 475 mV. In the following experiments, the detector was biased with the gate voltage of 475 mV, which represents the device's working regime with the best NEP values.
In the system with a VDI multiplier as a source, the TeraFET exhibited an optical voltage responsivity of 193 V/W (current responsivity of 38 mA/W) and a minimum optical NEP as low as 47 pW/ √ Hz at 609 GHz. It should be pointed out that the presented values are the optical ones for the detector module, i.e., in the calculation, we used the total available THz beam power at the position of the detector (measured after all OAP mirrors, attenuators, and other optical elements). Hence, the optical losses introduced by the detector module itself, such as in a silicon lens or radiation coupling to the integrated antenna, are not deducted. We also measured our detector's broadband performance in the Toptica system, where an original photomixer detector was replaced with the TeraFET (Figure 2b). The used sample exhibited a nearly flat frequency response characteristic from 0.4 up to 1.4 THz. The achieved minimum optical NEP was as low as 50 pW/ √ Hz at 0.6 THz and 81 pW/ √ Hz at 1.4 THz. The slightly worse detector characteristics in the Toptica system can be explained by a different beam profile and optical setup differences.

Experiment Setup for Homodyne Detection
For the characterization of the TeraFET's homodyne response in a broad frequency range from 0.1 up to 2.2 THz, we used two similar photomixer-based THz sources from the Toptica system in a homodyne scheme (TX1 and TX2, see Figure 1a) with a modulation frequency of 7.9 kHz. For the collimation and focusing of two THz beams onto the test detector, we constructed an imaging system with a two-inch diameter and four-inch effective focal length off-axis parabolic mirrors and a wire grid beamsplitter. The THz radiation is incident on the antenna from the detector's bottom through a hyper-hemispherical silicon lens and a reduced, 280 µm thick p-doped Si substrate of the chip. The lens has 12 mm diameter and 7.2 mm height with an additional 440 µm thick substrate. The THz beams are modulated electrically with a built-in function generator enabling to employ the lock-in amplifier.
Similarly, as it is used in a commercial photomixer-based system, we have not performed any additional effort regarding phase stabilization. We relied on a built-in laser control, which was developed by Toptica GmbH, providing good measurement-tomeasurement reproducibility of laser emission frequencies when the lasers are temperaturestabilized; additionally, the external conditions did not vary, thus maintaining the same spatial delay. In order to test the similarity of THz bias-modulated photomixers, we measured the frequency-dependent responses of the detector on both setup arms. The characterization results are presented in Figure 3a. Both sources provide a maximum THz output power at 100 GHz and fade out nearly exponentially with frequency. In a broad range, photomixers exhibited similar power levels except for a narrow band (120-350 GHz) where the difference reached 50%. The difference in the response values for TX1 and TX2 is related to the loss on a wire grid combiner and the differences in the individual sources' performances. The theory predicts that TeraFETs, when excited with low powers, behave as linear power detectors. The response linearity is maintained in different material systems [33] as well as for different biasing regimes [15,34]. The TeraFET's voltage signal is proportional to the THz beam power and can be expressed using (1) as: where the radiation power P THz is proportional to the squared excitation amplitude V THz . The difficulty of detecting a weak signal of sub-millimeter radiation can be reduced using a well-known homodyne technique. In a homodyne detection scheme, the detector is excited with two superimposed beams oscillating with the same angular frequency ω but differentiating in phase and/or amplitude (see Figure 1a). The phase can be introduced in the form of a difference in beam paths ∆L. The voltage signal of TeraFET can be defined by the following formula: where A 1 and A 2 are the amplitudes of the first and second beams, respectively, and k is a wavenumber, which is related to a wavelength λ or a frequency as k = 2π/λ = ω/c. The equation can be reduced to the following form: The first term is the average power. By changing frequency, the ω/c∆L varies from 0 to 2π, and the envelope of the detector's response dependency on an excitation frequency V det (ω) has a cosine form (so-called fringe spectrum, see the magnification in Figure 3b). We can also change a phase with mechanical XY stages or opaque materials, such as a paper Si attenuator.
The detector in the homodyne detection setup exhibits the same noise as for direct detection; however, it provides the difference signal in addition, which is not influenced by the noise of the THz source. The main advantage of homodyne detection is the ability to detect weaker excitation compared to a direct detection scheme.

Results and Discussions
The TeraFET response on the homodyne excitation at different gate bias voltages is presented in Figure 4a. For low gate voltages (below the threshold point at 445 mV), the voltage response is higher; however a signal-to-noise ratio (SNR) is lower due to an increase in noise. The SNR is defined as the ratio between the rms amplitude of the measured signal and the standard deviation of noise values. The best SNR for the investigated detector was obtained at a gate voltage bias of 475 mV. The graph also shows measured detector noise levels (dashed lines) obtained from the recorded statistics (standard deviation) of the response while blocking THz beams with an opaque metallic plate placed in front of the detector. These data allow calculating the dynamic range of device sensitivity as well as comparing with the theoretically expected thermal Johnson-Nyquist noise for the unbiased TeraFET's channel [35,36]. The theoretical noise voltage can be calculated using the simple equation V noise = 4k B TR DC ∆ f , where the equivalent noise bandwidth ∆ f in our case was equal to 1.25 Hz (for 100 ms integration time). V noise is shown in Figure 4a with hollow symbols. The measured detector noise levels correspond well to the theoretically expected thermal noise limit, which indicates good noise suppression techniques (such as shielding or removing ground loops) implemented in our setup, and validates the NEP results presented in Figure 2.
However, even when the detector noise was mainly of thermal origin, response curves showed similar additional signals at high frequencies (above 1.7 THz). The origin of this signal is not yet clearly understood. It can be either below 100 GHz as the result of beating between laser Fabry-Perrot modes or very broadband IR radiation from the local heating of the photomixer. There were several recent reports that the TeraFET detector could act as a detector of passive radiation [37,38]. The same is expected from Schottky-diode detectors.  Figure 4b shows the dynamic range of the measured response's dependency on the frequency for the gate voltage bias of 475 mV. The dynamic range reached a signal-tonoise ratio (SNR) of over 70 dB at 500 GHz and 100 ms integration time. The commercial homodyne system based on the same photomixer emitter and additional photomixer receiver can reach an SNR of ca. 83 dB, as declared by the manufacturer in the specification and confirmed by our independent tests. In our experimental work with one photomixerbased THz source [21], TereFET's SNR was 43 dB at 500 GHz and 100 ms. However, the commercial system uses a setup with four two-inches mirrors, which allows having the smallest losses in the optical path. The investigated system is based on a wire grid polarizer that divides each beam and total power in two. The second optical branch after the polarizer can be used in the future, for example, for additional reflection measurements.
The observed improvement in SNR of the TeraFET using the homodyne detection technique compared to the direct one could represent clearly seen water vapor lines [39] for frequencies over 2 THz, as shown in Figure 4b in comparison to Figure 3a. This allows us to conclude that these detectors can find practical application in continuous-wave THz spectrometry systems. Adding the second detector to the same system will allow to simultaneously record transmission and reflection amplitudes as well as propagation delay times, and therefore to measure complex dielectric properties as with heterodynebased vector network analyzers. TeraFETs have an advantage in comparison with other uncooled semiconductor THz power detectors in that they can be manufactured using mature commercial microchip mass-production technologies and hence can be realized as large-area matrices.

Conclusions
We demonstrated an effective homodyne detection system by employing a THz FET detector. The homodyne detection technique allows improving the SNR by up to 70 dB at the same frequency with a 100 ms integration time, which is more than 25 dB better than a direct detection system with the same components. The observed improvement in SNR using the homodyne technique with the TeraFET detector allows us to conclude that THz FET detectors can be successfully applied to continuous-wave THz spectrometry systems. Adding a second TeraFET detector to the same setup will allow us to simultaneously record transmission and reflection amplitudes as well as signal propagation delay times. Therefore, it opens the possibility to measure the complex dielectric properties of materials in the same way as with heterodyne-based vector network analyzers.  Acknowledgments: The authors would like to thank the THz research group from the University of Frankfurt, led by Roskos, for long-standing fruitful cooperation in developing THz detectors. The detector employed here was created within the scientific cooperation between the Frankfurt and Vilnius Universities' groups on a cost-sharing basis.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Abbreviations
The following abbreviations are used in this manuscript: THz terahertz FET field-effect transistor TeraFET field-effect transistor with integrated antennas for THz detection CMOS complementary metal-oxide-semiconductor Si silicon NEP noise-equivalent power SNR signal-to-noise ratio