HBT Amplifier Testing with the Zurich Instruments MFLI

In this repository I am testing an HBT based current preamplifier, designed to aid in measurements of an AC-SET charge sensor on silicon quantum dot devices. The amplifier is specifically meant to be running inside one of our He-4 cryostat probes at T = 1.4 K. Our cryostat is quite noisy, so the goal of this amplifier is to reduce the input referred noise spectrum from the charge sensor, in order to increase SNR at a given measurement bandwidth.

To achieve this goal, this repository runs the code for the room temperature and cryogenic tests. I am using a Femto labs DHCPA-100 trans-impedance amplifier (TIA) and a Zurich instruments MFLI lock-in amplifier. To power the DC bias current of the amplifier, I am using two Keithley 2401 source-measure units (SMU).

1. Room Temperature Measurements

The room temperature measurements were performed with the PCB in the unsealed cryostat probe. The output of the MFLI was fed into a 1/10,000 voltage divider,before being fed into a 50 $\mathrm{k\Omega}$ resistor. This resistor mimicks the usual conductance of a tuned SET charge sensor, and doubles as acurrent shunt resistor for the input current. The room temperature measurements were controlled via the notebook file HBT sweep.ipynb.

The primary purpose of the room temperature measurements were to demonstrate control over the instruments and to help inform my cryogenic measurements. The most helpful result of the room temperature tests were that the input impedance of the amplifier does not depend meaningfully on the bias current.

2. Cryogenic Measurements

The file that controls the measurements is the file cryo HBT test.ipynb, and the final plots are created by the file cryo/analysis.ipynb. The raw data is all in cryo/data.hdf5 and the finalized results are stored in cryo/hbt_characterization.hdf5

Unlike the room temperature measurements, for which I used a single SMU, the cryogenic measurements require a separate SMU for each of the two transistors. This is because the circuits of each stage are slightly different, and the transistors themselves are not matched perfectly, so the turn on bias required for each is ever so slightly different from one another. This does not matter at room temperature, since the thermal broadening means both transistors behave almost identically, turning on around 0.64 V. At cryogenic temperatures, the turn ons diverge slightly. So powering them both with the same bias voltage may mean one hits the compliance current before the other stage even activates.

Another difference is that we need come filtering on the bias lines coming out of the SMU. I used two RC low pass filters with a cutoff frequency of 1.6 Hz. They were a 10 $\mathrm{k\Omega}$ resistor and a 10 $\mathrm{\mu F}$ capacitor. The capacitor is large enough that it is essentially a short at the higher frequencies, so this hardly affects the input impedance of the amplifier. However, the extra voltage drop across the resistor means that this shifts the turn on votlages and makes the output current less sensitive to changes in bias voltage above the turn-on.

2.1 Setup

This time, the PCB itself contains the 50 $\mathrm{k\Omega}$ input resistor, mimicking the usual conductance range we expect to tune the SET charge sensors to. This was loaded into the cryostat and allowed to cool. Once at base temperature, the output of the MFLI was fed into a 1/10,000 voltage divider and then through a 10 $\mathrm{k\Omega}$ resistor, which acts as my input shunt resistor.

For output measurements, the output side of the amplifier is then fed into the TIA, whose output is in turn fed into the MFLI. For the input side measurements, I setup the MFLI to use a differential input, and measured across the shunt resistor.

2.2 Measurement Sequence

As outlined in the python notebook, the measurement sequence was as follows:

1. Connect to the SMUs, MFLI and the cryostat temperature controller
2. Create a bias voltage vs bias current calibration curve
   1. Measure the bias voltage vs bias current for both stages of the amplifier.
   2. Use isotonic regression to make the calibration curves for interpolation.
3. Measure the input current of the amplifier as a function of frequency and bias current
   1. Determine the small signal AC input impedance of the amplifier as a function of frequency
4. Measure the output current of the amplifier as a function of frequency and bias current
5. Noise plot of bias current and freq
   1. Determine the current gain
   2. Using the gain and the noise, determine the input referred noise density
   3. Choose the operating point with the lowest input referred noise density
6. Verify the linearity of the amplifier at the determined operating point

Output Measurement

(left) the output current as a function of bias current and frequency (right) the measured bias current for both transistors as a function of the intended setpoint: a test of the calibration.

2.3 Challenges

The main reason I chose this TIA and lock-in amplifier over the others we have in the lab are because of their higher bandwidths (1 MHz filter on the TIA, and 5 the MFLI has a 5 MHz BW). In previous tests, I have only had access to a DL instruments model 1211 current amplifier (20-30 kHz bandwidth) and the SR830 lock-in, which has a maximum frequency of 102 kHz. I thought that I could hopefully find a good operating point above the cutoff of the DL model 1211. However, the noise spectrum of our cryostat is very white, so by moving to a higher bandwidth TIA, a lot of high frequency reaches the input of the MFLI and overloads its input.

Because of the noise, I had to have a very modest gain no the TIA (1e-3 A/V) and a high input range (3V) for the MFLI. But with a 3 uA maximum output current of the amplifier, this is only going to be a 3mV RMS on the input of the MFLI. This means I am making very poor use of the input range of the MFLI. Since we still determined that the best operating point is probably around 10 kHz for this setup, future measurements will constrict the bandwidth to elimenate the high frequency noise.

I also had a couple of capacitors on the base of the transistors to dampen the high frequency noise, but I left those unpopulated for these experiments. In future tests, I will add these back in.

2.4 Results

The main take aways from both the cryogenic test and the room temperature test is that the input impedance of the amplifier does not appear to depend strongly on the bias current of the device. It also appears that the input referred noise of the devices is overwhelmed by the noise of the cryostat, and we cannot observe the increased shot and flicker noise of higher bias currents. Thus for our cryostat, the best operating point is somewhere in the 5-10 kHz range, and an appropriate bias between 5 and 15 uA can be chosen to obtain a specific gain or power dissipation.