Radio-frequency C-V measurements with sub-attofarad sensitivity

Abstract

We demonstrate the use of radio-frequency (rf) resonators to measure the capacitance of nanoscale semiconducting devices in field-effect transistor configurations. The rf resonator is attached to the gate or the lead of the device. Consequently, tuning the carrier density in the conducting channel of the device affects the resonance frequency, quantitatively reflecting its capacitance. We test the measurement method on InSb and InAs nanowires at dilution-refrigerator temperatures. The measured capacitances are consistent with those inferred from the periodicity of the Coulomb blockade of quantum dots realized in the same devices. In an implementation of the resonator using an off-chip superconducting spiral inductor we find sensitivity values reaching down to 75 zF/ √ Hz at 1 kHz measurement bandwidth, and noise down to 0.45 aF at 1 Hz bandwidth. We estimate the sensitivity of the method for a number of other implementations. In particular we predict typical sensitivity of about 40 zF/ √ Hz at room temperature with a resonator comprised of off-the-shelf components. Of several proposed applications, we demonstrate two: the capacitance measurement of several identical 80 nm-wide gates with a single resonator, and the field-effect mobility measurement of an individual nanowire with the gate capacitance measured in-situ.

Gate-Tunable Kinetic Inductance in Proximitized Nanowires

“…The measurement of the microwave kinetic inductance allows us to directly probe the bulk properties of the hybrid nanowires, in contrast with measurement on devices with etched Josephson junctions, which are affected by the junction geometry and fabrication details. Given that the kinetic inductance gives access to the normal-state conductivity in the proximitized nanowire, our method, if complemented with a capacitive measurement of the electron density via the bottom gate [60], could allow extraction of the mobility of the semiconductor under the Al shell. Such a measurement could be of relevance to determine whether the hybrid system meets the stringent disorder requirements for Majorana applications [61].…”

Gate-tunable kinetic inductance in proximitized nanowires

“…The measurement of the microwave inductance allows us to directly probe the bulk properties of the hybrid nanowire without the complications introduced by the fabrication and gate control of tunnel barriers. Our method, complemented by a capacitive measurement of the electron density via the bottom gate [59], could allow to extract the mobility of the semiconductor under the Al shell. Such a measurement could be of importance to determine whether the hybrid system meets the stringent disorder requirements for Majorana applications [60].…”