Single-electron Box Research Articles

Intrinsic noise of the single-electron box

The radio-frequency (rf) single-electron box is becoming an attractive charge sensor for semiconductor-based quantum computing devices due to its high sensitivity and small footprint, which facilitate the design of highly connected qubit architectures. However, an understanding of its ultimate sensitivity is missing due to the lack of a noise model. Here, we quantify the intrinsic noise of the single-electron box arising from stochastic cyclic electron tunneling between a quantum dot and a reservoir driven by a periodic gate voltage. We use both a master-equation formalism and Markov Monte Carlo simulations to calculate the gate-noise current and find that the noise mechanism can be represented as a cyclostationary process. We consider the implications of this cyclostationary noise on the ultimate sensitivity of single-electron box sensors for fast high-fidelity readout of spin qubits, in particular evaluating results for rf reflectometry implementations and the back action of the sensor on a qubit. Furthermore, we determine the conditions under which the intrinsic noise limit could be measured experimentally and techniques by which the noise can be suppressed to enhance qubit-readout fidelity. Published by the American Physical Society 2024

Nanoscale single-electron box with a floating lead for quantum sensing: Modeling and device characterization

We present an in-depth analysis of a single-electron box (SEB) biased through a floating node technique that is common in charge-coupled devices. The device is analyzed and characterized in the context of single-electron charge sensing techniques for integrated silicon quantum dots (QD). The unique aspect of our SEB design is the incorporation of a metallic floating node, strategically employed for sensing and precise injection of electrons into an electrostatically formed QD. To analyze the SEB, we propose an extended multi-orbital Anderson impurity model (MOAIM), adapted to our nanoscale SEB system, that is used to predict theoretically the behavior of the SEB in the context of a charge sensing application. The validation of the model and the sensing technique has been carried out on a QD fabricated in a fully depleted silicon on insulator process (FD-SOI) on a 22-nm CMOS technology node. We demonstrate the MOAIM's efficacy in predicting the observed electronic behavior and elucidating the complex electron dynamics and correlations in the SEB. The results of our study reinforce the versatility and precision of the model in the realm of nanoelectronics and highlight the practical utility of the metallic floating node as a mechanism for charge injection and detection in integrated QDs. Finally, we identify the limitations of our model in capturing higher order effects observed in our measurements and propose future outlooks to reconcile some of these discrepancies.

Fluctuations of heat in driven two-state systems: Application to a single-electron box with superconducting gap.

By using trajectory averaging to analyze the statistics of energy dissipation in the nonequilibrium energy-state transitions of a driven two-state system, we show that the average energy dissipation induced by external driving is connected to its fluctuations about equilibrium through the simple relation 2k_{B}T〈Q〉=〈δQ^{2}〉, which is preserved by an adiabatic approximation scheme. We use this scheme to obtain the heat statistics of a single-electron box with a superconducting lead in the slow-driving regime, where the dissipated heat becomes normally distributed with a relatively high probability to be extracted from the environment rather than dissipated. We also discuss the validity of heat fluctuation relations beyond driven two-state transitions and the slow-driving regime.

Fast High-Fidelity Single-Shot Readout of Spins in Silicon Using a Single-Electron Box

Three key metrics for readout systems in quantum processors are measurement speed, fidelity, and footprint. Fast high-fidelity readout enables midcircuit measurements, a necessary feature for many dynamic algorithms and quantum error correction, while a small footprint facilitates the design of scalable, highly connected architectures with the associated increase in computing performance. Here, we present two complementary demonstrations of fast high-fidelity single-shot readout of spins in silicon quantum dots using a compact, dispersive charge sensor: a radio-frequency single-electron box. The sensor, despite requiring fewer electrodes than conventional detectors, performs at the state of the art achieving spin readout fidelity of 99.2% in less than 6 μs fitted from a physical model. We demonstrate that low-loss high-impedance resonators, highly coupled to the sensing dot, in conjunction with Josephson parametric amplification are instrumental in achieving optimal performance. We quantify the benefit of Pauli spin blockade over spin-dependent tunneling to a reservoir, as the spin-to-charge conversion mechanism in these readout schemes. Our results place dispersive charge sensing at the forefront of readout methodologies for scalable semiconductor spin-based quantum processors.19 MoreReceived 7 May 2022Revised 4 December 2022Accepted 5 January 2023DOI:https://doi.org/10.1103/PhysRevX.13.011023Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum engineeringQuantum sensingRadio frequency techniquesPhysical SystemsNanotechnologyQuantum dotsCondensed Matter, Materials & Applied PhysicsQuantum Information

Ultimate Accuracy of Frequency to Power Conversion by Single-Electron Injection.

We analyze theoretically the properties of the recently introduced and experimentally demonstrated converter of frequency to power. The system is composed of a hybrid single-electron box with normal island and superconducting lead, and the detector of the energy flow using a thermometer on a normal metal bolometer. Here, we consider its potential for metrology. The errors in power arise mainly from inaccuracy of injecting electrons at the precise energy equal to the energy gap of the superconductor. We calculate the main systematic error in the form of the excess average energy of the injected electrons and its cumulants, and that due to subgap leakage. We demonstrate by analytic and numerical calculations that the systematic error in detection can, in principle, be made much smaller than the injection errors, which also, with proper choice of system parameters, can be very small, <1%, at low enough temperature. Finally, we propose a simplified configuration for metrological purposes.

Average electron number in two-island system

We studied the charge fluctuation in a two-metallic island system using a quantum Monte Carlo simulation. The imaginary-time path integral approach was used to express the system's grand canonical partition function. The average excess charge number on the islands was calculated using the distribution of the winding numbers. In the absence of a source-drain voltage, we found that an average electron number exhibited a Coulomb staircase phenomena and the function of the two gate voltages. Furthermore, as the temperature increased, the sharp step of the Coulomb staircase was smeared out. As a result, the system behaved as a single-electron box containing two coupled islands. We also suggest constructing a quantum stability diagram that accounts for the tunneling effect and temperature dependency from the average electron number. The calculation can be used to investigate the effect of the tunneling conductance on a honeycomb shape.

Gate reflectometry of single-electron box arrays using calibrated low temperature matching networks

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 1hbox {M}Omega. 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.

Asymmetric, mixed-valence molecules for spectroscopic readout of quantum-dot cellular automata

Mixed-valence compounds may provide molecular devices for an energy-efficient, low-power, general-purpose computing paradigm known as quantum-dot cellular automata (QCA). Multiple redox centers on mixed-valence molecules provide a system of coupled quantum dots. The configuration of mobile charge on a double-quantum-dot (DQD) molecule encodes a bit of classical information robust at room temperature. When arranged in non-homogeneous patterns (circuits) on a substrate, local Coulomb coupling between molecules enables information processing. While single-electron transistors and single-electron boxes could provide low-temperature solutions for reading the state of a ∼1 nm scale molecule, we propose a room-temperature read-out scheme. Here, DQD molecules are designed with slightly dissimilar quantum dots. Ab initio calculations show that the binary device states of an asymmetric molecule have distinct Raman spectra. Additionally, the dots are similar enough that mobile charge is not trapped on either dot, allowing device switching driven by the charge configuration of a neighbor molecule. A technique such as tip-enhanced Raman spectroscopy could be used to detect the state of a circuit comprised of several QCA molecules.

Thermodynamics of Gambling Demons.

We introduce and realize demons that follow a customary gambling strategy to stop a nonequilibrium process at stochastic times. We derive second-law-like inequalities for the average work done in the presence of gambling, and universal stopping-time fluctuation relations for classical and quantum nonstationary stochastic processes. We test experimentally our results in a single-electron box, where an electrostatic potential drives the dynamics of individual electrons tunneling into a metallic island. We also discuss the role of coherence in gambling demons measuring quantum jump trajectories.

Radio Frequency Reflectometry of Single-Electron Box Arrays for Nanoscale Voltage Sensing Applications

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 (&lt;0.01 µm2), a large number of devices (&gt;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.

A Review on Different Single Electron Devices and Their Comparative Study

Single Electron Devices being one of the nanodevices offers reduced feature size and low power consumption along with unique characteristics. The principle of operation is established upon the quantum mechanical tunneling of a single or few electrons for device switching between conducting and non-conducting state. The present work is a detailed survey on the different Single Electron Devices such as Single Electron Box, Double Tunnel Junction, Single Electron Transistor and Single Electron Turnstile. An overall comparative study of them is also furnished here as a fragment of the study. Keywords: Single Electron Box; Double Tunnel Junction; Single electron transistor; Single Electron Turnstile. Cite this Article: Bidisha Das, Riya Bandyopadhyay, Anamika Saha, Promit Das, Arpita Ghosh. A Review on Different Single Electron Devices and Their Comparative Study. International Journal Digital Communication and Analog Signals . 2020; 6(2): 21–27p.

Using single-electron box arrays for voltage sensing applications

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.

Room-temperature high sensitivity of multiple tunnel junctions based on single-charge photodetection

We successfully demonstrate the high stability at room temperature of a new design of single-photon detector based on multiple tunnel junctions with superior responsivity and high quantum efficiency. The single-photon detector uses one-dimensional (1D) multiple tunnel junctions (MTJs) with 12 islands and 13 tunnel junctions coupled with a silicon single-electron box. A single-electron transistor (SET) is used to read the charge state of a silicon quantum dot (Si-QD). The response of the single-photon detector (Si-QD and SET) is directly related to the photoconductivity gain in the MTJs with associated conductance steps produced by individual photocarriers. Numerical simulations confirm the high stability at room temperature of the single-photon detection. Moreover, an analytical model developed in MATLAB that takes account of the thermionic emission of charge carriers confirms the high stability of the single-photon detection at room temperature.

Orthodox Theory Monte-Carlo Simulation of Single-Electron Logic Circuits

In the past decades MOS based digital integrated logic circuits have undergone a successful process of miniaturisation eventually leading to dimensions of a few nanometres. With the dimensions in the range of a few atomic radii the end of conventional MOS technology is approaching. Amongst the prospective candidates for sub 10nm logic are integrated logic circuits based on single-electron devices. In our contribution we present the use of MOSES (Monte-Carlo Single-Electronics Simulator) as a method for simulation of complementary single-electron logic circuits based on the orthodox theory. Simulations of single-electron devices including a single-electron box, a single-electron transistor and a complementary single-electron inverter were carried out. Their characteristics were evaluated at different temperatures and compared to measurement results obtained at other institutions. The potential for room-temperature operation was also assessed.

All two-input logic gates by a single-stage single electron box

ABSTRACTIn this paper, the design of all two-input logic gates is presented by only a single-stage single electron box (SEB) for the first time. All gates are constructed based on a same circuit. We have used unique periodic characteristics of SEB to design these gates and present all two-input logic gates (monotonic/non-monotonic, symmetric/non-symmetric) by a single-stage design. In conventional monotonic devices, such as MOSFETs, implementing non-monotonic logic gates such as XOR and XNOR is impossible by only a single-stage design, and a multistage design is required which leads to more complexity, higher power consumption and less speed of the gates. We present qualitative design at first and then detailed designs are investigated and optimised by using our previous works. All designs are verified by a single electron simulator which shows correct operation of the gates.

Influence of measurement error on Maxwell's demon.

In any general cycle of measurement, feedback, and erasure, the measurement will reduce the entropy of the system when information about the state is obtained, while erasure, according to Landauer's principle, is accompanied by a corresponding increase in entropy due to the compression of logical and physical phase space. The total process can in principle be fully reversible. A measurement error reduces the information obtained and the entropy decrease in the system. The erasure still gives the same increase in entropy, and the total process is irreversible. Another consequence of measurement error is that a bad feedback is applied, which further increases the entropy production if the proper protocol adapted to the expected error rate is not applied. We consider the effect of measurement error on a realistic single-electron box Szilard engine, and we find the optimal protocol for the cycle as a function of the desired power P and error ɛ.

Inverse counting statistics based on generalized factorial cumulants

We propose a procedure to reconstruct characteristic features of an unknown stochastic system from the long-time full counting statistics of some of the system’s transitions that are monitored by a detector. The full counting statistics is conveniently parametrized by so-called generalized factorial cumulants. Taking only a few of them as input information is sufficient to reconstruct important features such as the lower bound of the system dimension and the full spectrum of relaxation rates. The use of generalized factorial cumulants reveals system dimensions and rates that are hidden for ordinary cumulants. We illustrate the inverse counting-statistics procedure for two model systems: a single-level quantum dot in a Zeeman field and a single-electron box subjected to sequential and Andreev tunneling.

Area efficient digital logic NOT gate using single electron box (SEB)

The continuing scaling down of complementary metal oxide semiconductor (CMOS) has led researchers to build new devices with nano dimensions, whose behavior will be interpreted based on quantum mechanics. Single-electron devices (SEDs) are promising candidates for future VLSI applications, due to their ultra small dimensions and lower power consumption. In most SED based digital logic designs, a single gate is introduced and its performance discussed. While in the SED based circuits the fan out of designed gate circuit should be considered and measured. In the other words, cascaded SED based designs must work properly so that the next stage(s) should be driven by the previous stage. In this paper, previously NOT gate based on single electron box (SEB) which is an important structure in SED technology, is reviewed in order to obtain correct operation in series connections. The correct operation of the NOT gate is investigated in a buffer circuit which uses two connected NOT gate in series. Then, for achieving better performance the designed buffer circuit is improved by the use of scaling process.

Distribution of current fluctuations in a bistable conductor

We measure the full distribution of current fluctuations in a single-electron transistor with a controllable bistability. The conductance switches randomly between two levels due to the tunneling of single electrons in a separate single-electron box. The electrical fluctuations are detected over a wide range of time scales and excellent agreement with theoretical predictions is found. For long integration times, the distribution of the time-averaged current obeys the large-deviation principle. We formulate and verify a fluctuation relation for the bistable region of the current distribution.

Short-time counting statistics of charge transfer in Coulomb-blockade systems

We study full counting statistics of electron tunneling in Coulomb-blockade systems in the limit of short measuring-time intervals. This limit is particularly suited to identify correlations among tunneling events, but only when analyzing the charge-transfer statistics in terms of factorial cumulants $C_{{\rm F}, m}(t)$ rather than ordinary ones commonly used in literature. In the absence of correlations, the short-time behavior of the factorial cumulants is given by $C_{{\rm F}, m}(t) \propto (-1)^{m-1}t^m$. A different sign and/or a different power law of the time dependence indicates correlations. We illustrate this for sequential and Andreev tunneling in a metallic single-electron box.