No abstract

Single-electron tunneling transistors (SETs) and boxes (SEBs) belong to the family of charge-sensitive electronic devices based on the phenomenon of Coulomb blockade. An SEB is a two-terminal device composed of “leaky,” Cj, and “non-leaky,” Cg, nanoscaled capacitors in series. At low temperatures, the charge at the common node is quantized and can only be changed near energy-population degeneracy points, resulting in periodic oscillations of the SEB admittance as a function of voltage applied to Cg. In comparison to the SETs, SEBs have higher operating temperature, are electrostatic discharge tolerant, and have a much smaller footprint. To monitor the SEB admittance, Radio Frequency reflectometry can be used. To improve the signal-to-noise ratio, limited by the small change in admittance in an SEB, multiple devices sharing the same source and gate electrodes are connected in parallel to form arrays of SEBs. Due to unavoidable random offset charges, the signal boost for an array of N SEBs is expected to be ∼N. We experimentally demonstrate that by carefully choosing the operating point, the response to the voltage on the sensing gate can be enhanced, for small arrays scales, by a factor approaching N and, thus, provides a method by which these devices can be used in practical sensing applications, such as a scanning probe.

Single-electron tunneling transistors (SETs) and boxes (SEBs) exploit the phenomenon of Coulomb blockade to achieve unprecedented charge sensitivities. Single-electron boxes, however, despite their simplicity compared to SETs, have rarely been used for practical applications. The main reason for that is that unlike a SET where the gate voltage controls conductance between the source and the drain, an SEB is a two terminal device that requires either an integrated SET amplifier or high-frequency probing of its complex admittance by means of radio frequency reflectometry (RFR). The signal to noise ratio (SNR) for a SEB is small, due to its much lower admittance compared to a SET and thus matching networks are required for efficient coupling ofSEBs to an RFR setup. To boost the signal strength by a factor of N (due to a random offset charge) SEBs can be connected in parallel to form arrays sharing common gates and sources. The smaller the size of the SEB, the larger the charging energy of a SEB enabling higher operation temperature, and using devices with a small footprint (<0.01 µm2), a large number of devices (>1000) can be assembled into an array occupying just a few square microns. We show that it is possible to design SEB arrays that may compete with an SET in terms of sensitivity. In this, we tested SETs using RF reflectometry in a configuration with no DC through path (“DC-decoupled SET” or DCD SET) along with SEBs connected to the same matching network. The experiment shows that the lack of a path for a DC current makes SEBs and DCD SETs highly electrostatic discharge (ESD) tolerant, a very desirable feature for applications. We perform a detailed analysis of experimental data on SEB arrays of various sizes and compare it with simulations to devise several ways for practical applications of SEB arrays and DCD SETs.

Sensitive dispersive readouts of single-electron devices (“gate reflectometry”) rely on one-port radio-frequency (RF) reflectometry to read out the state of the sensor. A standard practice in reflectometry measurements is to design an impedance transformer to match the impedance of the load to the characteristic impedance of the transmission line and thus obtain the best sensitivity and signal-to-noise ratio. This is particularly important for measuring large impedances, typical for dispersive readouts of single-electron devices because even a small mismatch will cause a strong signal degradation. When performing RF measurements, a calibration and error correction of the measurement apparatus must be performed in order to remove errors caused by unavoidable non-idealities of the measurement system. Lack of calibration makes optimizing a matching network difficult and ambiguous, and it also prevents a direct quantitative comparison between measurements taken of different devices or on different systems. We propose and demonstrate a simple straightforward method to design and optimize a pi matching network for readouts of devices with large impedance, $$Z \ge 1\hbox {M}\Omega$$ Z ≥ 1 M Ω . It is based on a single low temperature calibrated measurement of an unadjusted network composed of a single L-section followed by a simple calculation to determine a value of the “balancing” capacitor needed to achieve matching conditions for a pi network. We demonstrate that the proposed calibration/error correction technique can be directly applied at low temperature using inexpensive calibration standards. Using proper modeling of the matching networks adjusted for low temperature operation the measurement system can be easily optimized to achieve the best conditions for energy transfer and targeted bandwidth, and can be used for quantitative measurements of the device impedance. In this work we use gate reflectometry to readout the signal generated by arrays of parallel-connected Al-AlOx single-electron boxes. Such arrays can be used as a fast nanoscale voltage sensor for scanning probe applications. We perform measurements of sensitivity and bandwidth for various settings of the matching network connected to arrays and obtain strong agreement with the simulations.