Integrated impedance bridge for absolute capacitance measurements at cryogenic temperatures and finite magnetic fields

Abstract

We developed an impedance bridge that operates at cryogenic temperatures (down to 60 mK) and in perpendicular magnetic fields up to at least 12 T. This is achieved by mounting a GaAs HEMT amplifier perpendicular to a printed circuit board containing the device under test and thereby parallel to the magnetic field. The measured amplitude and phase of the output signal allows for the separation of the total impedance into an absolute capacitance and a resistance. Through a detailed noise characterization, we find that the best resolution is obtained when operating the HEMT amplifier at the highest gain. We obtained a resolution in the absolute capacitance of 6.4 aF/ √ Hz at 77 K on a comb-drive actuator, while maintaining a small excitation amplitude of 15 k B T /e. We show the magnetic field functionality of our impedance bridge by measuring the quantum Hall plateaus of a top-gated hBN/graphene/hBN heterostructure at 60 mK with a probe signal of 12.8 k B T /e.

Nanoelectromechanical Sensors Based on Suspended 2D Materials

“…For readout, it requires detecting a small capacitance change on a large parasitic background capacitance. Even when using insulating quartz substrates to reduce the parasitic capacitance [ 182 ], it is difficult to measure the capacitance changes, since responsivities of a drum with a 5 micron diameter are at most 0.1 aF/Pa, which at a voltage of 1.6 V corresponds to only 1 electron moving onto the graphene for a pressure change of 1 Pa. By utilizing a high-frequency AC signal to charge and discharge the capacitor many cycles, signal-to-noise ratios can be improved to achieve a resolution of 2-4 aF/√Hz, requiring at least 20-40 of these drums in parallel to reach a pressure resolution of 1 Pa with an acquisition time of 1 second [ 192 ]. Recently, capacitive pressure sensors have been reported with many graphene drums in parallel that outperform the best commercial capacitive pressure sensors (SBC10 of Murata, responsivity 55 aF/Pa [ 184 ]) and that could be read out using a commercial IC [ 193 ].…”

High Precision, Low Excitation Capactiance Measurement Methods from 10 mK- to Room-Temperature

“…In order to reduce the crosstalk and signal leaking between cables, many reported works use the cryogenic preamplifier to isolate the input and output signals 5,10,11,17,18 . Unfortunately, the preamplifiers usually dissipate more than ∼10 µW heat at the sample stage, which is sufficiently high to cause a noticeable temperature raise.…”