2.1. HEB mixer design

The 0.2–2 THz superconducting HEB device consists of a NbN micro-bridge and a planar spiral antenna. The NbN micro-bridge, located at the center of the planar spiral antenna, has a width of 2 μm and a length of 0.2 μm. The thickness of the NbN film is 5.5 nm and is connected to the spiral antenna by two Ti/Au pads. Both micro-bridge and spiral antenna are fabricated on the high-resistivity silicon substrate.

Figure 1 presents the SEM picture (inset image) of the superconducting HEB device. The spiral antenna arms are defined by r₁ = ke^aφ and r₂ = ke^a(φ – δ), where r₁ = 120 μm is the outer radius, r₂ = 3.6 μm is the inner radius, k = 4 μm is the initial inner radius, a = 0.35 is the growth rate, and φ is the angular position. The simulated input resistance and reactance of the spiral antenna are shown in Fig. 2, the resistance is nearly constant (∼ 80 Ω) in the whole operating frequency range.

The measured R–T and I–V curves of the HEB device are presented in Figs. 1 and 3, respectively. The critical temperature T_c is around 9 K, and the critical current I_c is around 100 μA at 4 K. The normal state resistance is about 160 Ω, as shown in Fig. 1.

2.2. Measurement setup

The double sideband (DSB) receiver noise temperatures of the 0.2–2 THz HEB mixer are measured at 0.2 THz, 0.5 THz, 0.85 THz, and 1.34 THz by the Y-factor method. The measurement system is illustrated in Fig. 4. The HEB device is stuck to the flat surface of a Si elliptical lens which has a long axis length of 5.228 mm and a minor axis length of 5 mm, the extension length is 1.149 mm. The lens, without anti-reflection coating, is mounted in a cupreous mixer block which is mounted in a close-cycled cryostat. A Zitex G104 film is used to filter the infrared radiation and a HDPE sheet with a thickness of 1.5 mm is employed as the vacuum window of the cryostat. The LO and RF signals are coupled to the HEB mixer by a 25 μm Mylar film. The LO signals are provided by a signal generator together with different frequency multiplier chains.

The intermediate frequency (IF) output signal from the HEB mixer is amplified firstly by a low noise amplifier (LNA) and then a room temperature amplifier. The amplified IF power is then filtered by a bandpass filter (80 MHz) at 1.5 GHz and recorded by a square-law detector.

Figure 3 shows the measured I–V curves of the HEB mixer at 0.2 THz and 0.85 THz with different local oscillator pumping levels. It is obvious that the well-pumped I–V curves at 0.2 THz still show negative resistances, which can be attributed to the non-uniformly absorption of LO power in the NbN micro-bridge.^[14] The DSB noise temperatures T_rec have been measured at these pumping levels (shown in Fig. 3), and are then plotted in a two-dimensional graph of the bias voltage and current in order to get a better view of its dependence on bias points. At each fixed bias voltage, the noise temperature distribution corresponding to different bias currents (or LO pumping levels) is obtained by linear interpolation of the measured data.

3.1. Optimal bias region

The DSB receiver noise temperatures have been measured at a large number of bias points at four frequencies, and are illustrated in Fig. 5. The effective radiation temperatures of 300 K and 77 K (blackbody) are calculated based on the Callen–Welton definition^[15] at each LO frequency in the Y-factor method. What is more, the compensation of the direct detection effect is fulfilled by keeping the bias current unchanged between the 300 K and 77 K blackbody measurements.^[16] A broad optimal bias range can be observed at each frequency, indicating a good bias applicability of the HEB mixer for multipixel application. Note that, the bias current of the HEB mixer (Y axis in Fig. 5) has been normalized to the critical current I_c for universal comparison. A raised region (marked by circle) at low bias voltage can be observed at 0.2 THz and 0.5 THz, which can be attributed to the negative resistance region as shown in the measured I–V curves. The lowest uncorrected DSB noise temperatures at these frequencies are also listed in Table 1, indicating that this HEB mixer has high sensitivity in the whole operating frequency range. The noise temperature at 1.34 THz is slightly higher than that at other frequencies, which is because the RF loss of 25 μm Mylar at 1.34 THz is higher than that at other frequencies (as shown in Table 2).

3.2. Frequency dependence of HEB mixer noise temperature

The measured DSB receiver noise temperature T_rec includes three parts: RF noise T_RF, HEB mixer intrinsic noise T_mixer, and IF noise T_IF, and can be expressed as

where G_RF is the RF loss, and G_mixer is the conversion gain of the HEB mixer. In order to investigate the distribution of HEB mixer noise temperature T_mixer, we need to calibrate other noises.

The IF noise T_IF is mainly produced by the LNA and is normally very small (about 3–4 K). The conversion gain G_mixer of the HEB mixer is about –5 dB and is proved to be frequency independent.^[14] Therefore we ignore the term T_IF/G_mixer in Eq. (1) and focus on the calibration of RF loss G_RF and RF noise T_RF.

The RF noise is produced by the RF optics in the receiver system which consists of a 25 μm Mylar beam splitter, a 1.5 mm HDPE window, a Zitex G104 infrared filter, an air path, a Si lens, and a planar spiral antenna. The equivalent input noise temperature T_eq of each RF component with a gain G is given by

According to Eq. (2), the gain G of each RF component is the most crucial parameter. In order to obtain a precise value of the RF loss, we measure and simulate the transmittance of all RF components, as shown in Figs. 6 and 7. The transmittances of the Mylar and Zitex films are measured by a time-domain spectrometer (TDS), and the complex permittivity is derived from the measured result. The simulation of transmittance is performed by FEKO software^[17] with measured complex permittivity, and as shown in Fig. 6 good agreement has been found between simulation and measurement. The transmittance of HDPE has been measured in Ref. [11]. The transmittance of the air path is calculated by an atmospheric model (AM).^[18] The coupling efficiency between the planar spiral antenna and superconducting NbN film has been measured by a FTS with a calibration method described in Ref. [19]. The measured coupling efficiency of the spiral antenna shows the same trend with the simulation one, where the difference is largely due to the water absorption in the air path, as shown in Fig. 7. The reflection loss of the air and Si lens interface on both sides is about 1.54 dB according to the measurements in Ref. [20], where the absorption loss inside the high resistivity silicon material is ignored. All measured and simulated RF losses are listed in Table 2.

After calibrating the RF noise and RF loss by Eqs. (1) and (2), we plot the HEB mixer noise temperature in a two-dimensional graph of the bias voltage and current at 0.2 THz, 0.5 THz, 0.85 THz, and 1.34 THz in Fig. 8. The corrected mixer noise temperature shows the same distribution on bias point at all frequencies, in other words a frequency independent optimal bias region has been observed. The corrected lowest noise temperature has also been listed in Table 1, a frequency independent mixer noise temperature has been obtained without considering the quantum noise contribution.

3.3. Bath temperature dependence

The receiver noise temperature of the superconducting HEB mixer has also been measured at 4 K, 5 K, 6 K, and 7 K to investigate the effect of the bath temperature on the optimal bias region. Figure 9 shows the DSB receiver noise temperatures distribution at different bath temperatures at 0.85 THz. Note that similar phenomenon has been observed at other frequencies, we only plot the result at this frequency for illustration. Figure 10 illustrates the bath temperature dependence of the measured results. The lowest receiver noise temperature T_rec only increases from 750 K to 810 K when the bath temperature increases to 6 K, however it rapidly raises to 1000 K when the bath temperature increases to 7 K due to the rapid decrease of the critical current of the HEB mixer. The optimal bias area, defined as the bias region where the noise temperature is lower than 900 K, has been calculated by counting the bias points with a voltage interval of 0.1 mV and a current interval of 0.01 × I/I_c. Obviously, the optimal bias points decrease rapidly with increasing bath temperature. In conclusion, we believe that the bath temperature has limited effect on the lowest receiver noise temperature until it raises to 7 K (about 0.8 times critical temperature T_c^[21]), however the optimal bias region deteriorates obviously with increasing bath temperature.