Figure 1(a) shows the schematic diagram of our amplifier and the layout of the amplifier. The amplification line consists of two parts interconnected by two coaxial cables (50-Ω impedance), as shown in the circuit schematic diagram in Fig. 1(a). The cryogenic part is thermally anchored to the cold finger of our home-made liquid helium dip stick. The room temperature part consists of two variable resistors and a 12-V lead-acid battery, which are in an aluminum box for shielding. The cryogenic part is made on a one-side surface copper coating printed-circuit board (FR-4 glass epoxy) with commercial discrete components and it is placed in a copper shielding box (the outer size is 20 mm×31 mm) as shown in Fig. 1(c). Four SMB connectors interconnect the amplifier and the outside of the copper shielding box. Figure 1(b) shows a schematic of the printed-circuit board. The size of the printed-circuit board is 10 mm×20 mm and the metal (yellow regions) is patterned by chemical etching. The HEMT (Agilent ATF-34143) is the only active component in the circuit. All the cryogenic resistors are Susumu 0805-size surface mount thin metal film resistors from Mouser electronics. The cryogenic capacitors are 0805-size surface mount (Murata C0G GRM2165 multilayer ceramic capacitor) except C _in, which is a leaded ceramic capacitor that protects the HEMT from breakdown. Two sets of 10-Ω resistors and 100-nF capacitors are used for the two source leads of ATF-34143 to avoid the interference of the ground. These passive components with small temperature coefficients play a role in stabilizing the amplifier.

Fig. 1.

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	Fig. 1. (color online) (a) Circuit schematic diagram of our amplifier. (b) Layout of the CRYOAMP circuit board. Metal (yellow regions) is patterned by etching one-side surface copper coating FR-4 glass epoxy, whose size is 1 cm×2 cm. Four red points show the solder points on the printed-circuit board, which connect the inner pin of the connector. (c) Photograph of a CRYOAMP circuit board.

The HEMT must be biased in saturation to provide voltage (transconductance) gain in the low (high) frequency range. Figure 2 shows the DC characteristics of the cryogenic part of the amplifier at (a) room temperature and (b) liquid helium temperature. V _d−10R is the voltage between the drain of HEMT and the 10-Ω resistor R _n2, and V _g is the voltage between the gate and ground. According to previous implementations of the similar circuits, the DC characteristics of the HEMT varies a little.^[16,17] However, the large V _d−10R can cause a shift in the dc characteristics at the low temperature. If we bias the I _ds between 0.2 mA ∼ 0.8 mA, we can estimate that the transconductance of the HEMT is about 5 mS ∼ 20 mS, which is slightly smaller at room temperature (RT) than at liquid helium temperature, as shown in Fig. 2. The room temperature part in Fig. 1(a) that consists of a 12-V lead-acid battery and two variable resistors determine the HEMT operating point. Thus we choose proper R _s (880 Ω at room temperature and 500 Ω at liquid helium temperature) and proper R _d to bias the HEMT to the proper quiescent operating point (V _d−10R ∼ 0.2 V, I _ds ∼ 0.6 mA). The gain of the HEMT amplifier is 0.5 and flat in the frequency range of interest (500 kHz to 8 MHz) at liquid helium temperature, which is measured by a function generator and 50 MHz digitizer with an input impedance of 50 Ω. The result is shown in Fig. 3. The DC equivalent effective circuit is shown in Fig. 4(a) and the AC equivalent effective circuit is shown in Fig. 4(b). The output signal of the HEMT amplifier is amplified by a 50-Ω amplifier with a gain of 60 dB at room temperature.

Fig. 2.

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	Fig. 2. (color online) Typical DC characteristics of the cryogenic part of the amplifier at (a) room temperature and (b) liquid helium temperature. (a) V g varies from −0.40 V (top) to −0.75 V (bottom) in 0.01-V steps. (b) V g varies from −0.25 V (top) to −0.49 V (bottom) in 0.01-V steps.

Fig. 3.

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	Fig. 3. (color online) The frequency dependence of the voltage gain of the cryogenic amplifier into a 50-Ω load, measured for the quiescent operating points at room temperature (red line), liquid nitrogen temperature (green line), and liquid helium temperature (blue line).

Fig. 4.

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	Fig. 4. (color online) Equivalent effective circuits: (a) DC bias circuits and (b) AC signal circuits.

Our noise measurement system is installed on our home-made liquid helium dip stick. The cryogenic part in Fig. 1(a) is thermally anchored to the cold finger. Figure 5 shows the schematic of our measurement setup. We use a voltage source and a 1-MΩ ballast resistor in series to supply the current. For the transport measurement, we use a digital voltage meter (DVM) to measure the voltage. Since the capacitance of the transport line can shunt the noise signal of the sample for the noise measurement, we use two cryogenic resistors (15-kΩ Susumu 0805-size thin metal film resistor) with resistance similar to that of the sample in series, and fix them on the sample holder close to the sample, as shown in the left part of Fig. 5. For the noise measurement, the noise signal of the sample is amplified by our cryogenic amplifier at liquid helium temperature and the 50-Ω amplifier (MITEQ AU-1447) with a gain of 60 dB and a noise temperature of 92.3 K in the range of 0.01 MHz–200 MHz, then the time domain signal is taken by a data acquisition card (ADLINK PCI-9846H/512), as shown in the right part of Fig. 5. Then we obtain the spectrum and power spectrum density by performing the fast fourier transformation (FFT) for the data. Impedance matching to avoid signal attenuation is taken into account as the input impedance and the output impedance of the Au-1447 is 50 Ω. To block the dc current, we use a DC block (Mini-circuits BLK-89-S+ with the range of 0.1 MHz–8000 MHz) between the cryogenic amplifier and the Au-1447 amplifier. To avoid the frequency aliasing, we use an anti-aliasing filter (Mini-circuits BLP-10.7+ low pass filter) between the data acquisition card and the Au-1447 amplifier. According to the measured frequency dependence of the gain of the HEMT amplifier in Fig. 3, we estimate the frequency dependence of the total gain of the system with the same method. Although it is not constant in the frequency range of interest (500 kHz to 8 MHz), it is flat enough to average for the frequency bin we select, 2 MHz to 2.1 MHz, the gain is about 590. The total gain is also calibrated by the thermal noise measurement for 10 Ω, 1 kΩ, 5 kΩ, 10 kΩ thin film resistors at room temperature and liquid helium temperature.

Fig. 5.

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	Fig. 5. (color online) Schematic diagram of the measurement setup with the transport measurement part and the noise measurement part. The transport measurement includes four lines (twisted pair cable), while the noise measurement includes four coaxial cables. Only one coaxial cable which is as output line is shown in this figure for simplicity.

We demonstrate the performance of our noise measurement system by measuring shot noise on a tunneling junction. The tunneling junction is fabricated on one-side polished silicon covered by a 300-nm oxidized layer. In order to create a very clean interface of the oxidation layer and a well-controlled tunneling junction, we use the shadow evaporation method, in which the top layer aluminum film was deposited on the bottom layer aluminum film at different angles through a shadow mask after in-situ oxidation of the bottom layer aluminum without breaking the vacuum.^[20–23] The shadow mask is defined by PMGI/PMMA bilayer electron-beam lithography on the Ti/Au pad for wire bonding, which is fabricated by standard bilayer UV lithography and lift-off techniques, as shown in Figs. 6(a) and 6(b). To test our amplifier, we choose the resistance of the tunneling junction to be ∼10 kΩ, because large resistance of the tunneling junction limits the bandwidth of the observed spectrum, while smaller sample resistance makes it difficult for the amplification to measure the current noise. Thus we choose the deposition and oxidation parameter carefully. To maintain directional deposition and less coating on side walls, aluminum films are deposited at ∼1 Å/s by the thermal evaporator system with base pressure below 1 × 10⁻⁶ Torr (1 Torr = 1.33322×10² Pa). To ensure the ohmic contact, we deposit 28-nm first layer aluminum film along the direction normal to the substrate with 25-nm Ti/Au pad, and 50-nm second layer aluminum film at a 30° angle to the substrate and parallel slit in Fig. 6(a). To ensure the uniform oxidation and avoid the pin holes in the oxidation layer, the first layer aluminum is oxidized in 1.92-Torr argon mixed with 0.338-Torr oxygen for 3 min. The area of the tunneling junction is controlled by the geometry of the shadow mask and the deposition angles of the second layer aluminum. The scanning electron microscopy (SEM) image of Al/AlO_x/Al tunneling junction is shown in Fig. 6(c).

Fig. 6.

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Fig. 6. (color online) Fabrication of Al/AlOx/Al tunneling junction. (a) SEM image of the shadow mask taken after the deposition of Aluminum films and before lift-off. The bilayer shadow mask consists of a top 200-nm thick polymethyl methacrylate (950 A4 PMMA) layer, used as a high-resolution electron resist, and a bottom 400-nm thick layer of polymer polydimethylglutarimide (PMGI SF6). A deep undercut in the bottom layer allows for overlapping of the films deposited at different incident angles. (b) Cross-section along the dashed line in panel (a). The first layer Al is deposited along the direction normal to the plane of the substrate, the second layer Al is deposited at a 30° incidence angle and parallel slit in panel (a). (c) SEM image of Al/AlOx/Al tunneling junction with dimensions 180 nm×1000 nm×70 nm. The 1st layer Al and the 2nd layer Al overlap on the different Ti/Au pattern leads, which we fabricated by UV lithography.

Differential resistance measurement is performed with conventional lock-in techniques. The part of the circuit for transport measurement is shown in Fig. 5. Figure 7 shows the differential resistance of the tunneling junction as a function of temperature during warming up, which is typical for this kind of junction. The upper inset shows the SEM images of the device we measured. The lower inset shows the differential resistance as a function of the current bias at 4.6 K.

Fig. 7.

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	Fig. 7. (color online) Differential resistance as a function of temperature. Inset: Upper right shows the SEM image of the Al/AlOx/Al tunneling junction (red circle). Lower left shows the differential resistance as a function of the current bias at 4.6 K.

We measured the total noise spectral density at 4.6 K and normalized them using the total gain of our noise measurement setup at 2 MHz as an equivalent input referred voltage noise, which is shown in Fig. 8(a). A characteristic 1/f contribution is present up to 100 kHz. The drop of the noise power from 100 Hz to 1000 Hz is caused by the DC block in Fig. 5. The spectrum from 100 kHz to 2 MHz is dominated by the thermal noise of the system and the shot noise of the junction. The spectrum also reveals the change of the voltage gain of the HEMT.^[16] The extra noise over 2 MHz may be caused by the shielding problem or resonance effect with the filter. We pick the spectrum in the frequency bin, 2 MHz to 2.1 MHz, that is flat enough to average, as shown in the inset in Fig. 8(a). The bias dependence of the voltage noise power that is related to the current noise power S _I by is plotted in Fig. 8(b). R _d is the differential resistance of the tunneling junction, as shown in the inset in Fig. 7. The current noise power S _I is fitted using the following equation by considering the contribution of the background noise (including the thermal noise of the system) of the system.^[24] 1 where F is the Fano factor, T is device temperature, which is measured by the Cernox-1070 thermometry mounted on the cold finger, and k _B is the Boltzmann constant. The Fano factor F and the background noise BG (include the thermal noise of the system) of the system are the fitting parameters. Using Eq. (1), we can fit the Fano factor F of the Al/AlO_x/Al tunneling junction and the background noise BG. The results are shown in Fig. 8(b), F is 0.998, and BG is . We also select other frequency bins to average and conduct similar fitting using the total gain in Subsection 3.1 (details are given in Appendix A). The results are consistent.

Fig. 8.

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Fig. 8. (color online) (a) Voltage noise spectrum for different current bias of the Al/AlOx/Al tunneling junction at 4.6 K, which is measured by our cryogenic amplifier with Au-1447 amplifier. Current bias varies from 0 μA to 1 μA in 0.05-μA steps. Inset: Zoom-in of the voltage noise spectrum in the frequency bin we pick with linear axis, 2.0 MHz to 2.1 MHz (black rectangle). (b) The bias dependence of the voltage noise power of the Al/AlOx/Al tunneling junction at 4.6 K measured by our cryogenic amplifier with Au-1447 amplifier.

For comparison, we have conducted a similar measurement using a different noise measurement setup, which consists of our home-made room temperature pre-amplifier (the input impedance of the amplifier is 100 MΩ) and data acquisition card (National Instruments PCI-4474).^[25,26] The voltage noise spectrum that is normalized by the gain of the home-made room temperature pre-amplifier at 1 kHz for different current bias is shown in Fig. 9(a). The voltage noise power differs by an order of magnitude from Fig. 8(a) because of the different input impedance of the amplifier. The inset shows the spectrum in the frequency bin we pick, 1 kHz to 1.5 kHz, that is flat enough to average. The fitting results are shown in Fig. 9(b). The Fano factor F is 0.964 that is consistent with the results in Fig. 8(b), while the background noise BG is 3.094 , which is larger than that in Fig. 8(b).

Fig. 9.

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Fig. 9. (color online) (a) Voltage noise spectrum for different current bias of the Al/AlOx/Al tunneling junction at 4.6 K, which is measured by our room temperature pre-amplifier. Current bias varies from 0 μA to 1 μA in 0.05-μA steps. Inset: Zoom-in of the voltage noise spectrum in the frequency bin we pick with linear axis, 1.0 kHz to 1.5 kHz (black rectangle). (b) The bias dependence of the voltage noise power of the Al/AlOx/Al tunneling junction at 4.6 K measured by our room temperature pre-amplifier.