Single-electron Charging Research Articles

Scanning-probe Single-electron Capacitance Spectroscopy

The integration of low-temperature scanning-probe techniques and single-electron capacitance spectroscopy represents a powerful tool to study the electronic quantum structure of small systems - including individual atomic dopants in semiconductors. Here we present a capacitance-based method, known as Subsurface Charge Accumulation (SCA) imaging, which is capable of resolving single-electron charging while achieving sufficient spatial resolution to image individual atomic dopants. The use of a capacitance technique enables observation of subsurface features, such as dopants buried many nanometers beneath the surface of a semiconductor material(1,2,3). In principle, this technique can be applied to any system to resolve electron motion below an insulating surface. As in other electric-field-sensitive scanned-probe techniques(4), the lateral spatial resolution of the measurement depends in part on the radius of curvature of the probe tip. Using tips with a small radius of curvature can enable spatial resolution of a few tens of nanometers. This fine spatial resolution allows investigations of small numbers (down to one) of subsurface dopants(1,2). The charge resolution depends greatly on the sensitivity of the charge detection circuitry; using high electron mobility transistors (HEMT) in such circuits at cryogenic temperatures enables a sensitivity of approximately 0.01 electrons/Hz(½) at 0.3 K(5).

Thermodynamic and quantum bounds on nonlinear dc thermoelectric transport

I consider the non-equilibrium DC transport of electrons through a quantum system with a thermoelectric response. This system may be any nanostructure or molecule modeled by the nonlinear scattering theory which includes Hartree-like electrostatic interactions exactly, and certain dynamic interaction effects (decoherence and relaxation) phenomenologically. This theory is believed to be a reasonable model when single-electron charging effects are negligible. I derive three fundamental bounds for such quantum systems coupled to multiple macroscopic reservoirs, one of which may be superconducting. These bounds affect nonlinear heating (such as Joule heating), work and entropy production. Two bounds correspond to the first law and second law of thermodynamics in classical physics. The third bound is quantum (wavelength dependent), and is as important as the thermodynamic ones in limiting the capabilities of mesoscopic heat-engines and refrigerators. The quantum bound also leads to Nernst's unattainability principle that the quantum system cannot cool a reservoir to absolute zero in a finite time, although it can get exponentially close.

Powerful and efficient energy harvester with resonant-tunneling quantum dots

We propose a nanoscale heat engine that utilizes the physics of resonant tunneling in quantum dots in order to transfer electrons only at specific energies. The nanoengine converts heat into electrical current in a multiterminal geometry which permits one to separate current and heat flows. By putting two quantum dots in series with a hot cavity, electrons that enter one lead are forced to gain a prescribed energy in order to exit the opposite lead, transporting a single electron charge. This condition yields an ideally efficient heat engine. The energy gain is a property of the composite system rather than of the individual dots. It is therefore tunable to optimize the power while keeping a much larger level spacing for the individual quantum dots. Despite the simplicity of the physical model, the optimized rectified current and power is larger than any other candidate nanoengine. The ability to scale the power by putting many such engines into a two-dimensional layered structure gives a paradigmatic system for harvesting thermal energy at the nanoscale. We demonstrate that the high power and efficiency of the layered structure persists even if the quantum dots exhibit some randomness.

Electrochemical Resolution of Multiple Redox Events for Graphene Quantum Dots

Quantum dots: A sequential, single-electron charging process of monodisperse graphene quantum dots (GQDs) encapsulated in a dodecylamine envelope, facilitating a capacitance of a few attofarads is reported. The average GQDs dimensions, as ascertained from high-resolution transmission electron microscopy and atomic force microscopy, of about 3±0.3, 2.6±0.2, and 2.2±0.3 nm control this unprecedented behavior.

Negative Differential Photoconductance in Gold Nanoparticle Arrays in the Coulomb Blockade Regime

We investigate the photoconductance of gold nanoparticle arrays in the Coulomb blockade regime. Two-dimensional, hexagonal crystals of nanoparticles are produced by self-assembly. The nanoparticles are weakly coupled to their neighbors by a tunneling conductance. At low temperatures, the single electron charging energy of the nanoparticles dominates the conductance properties of the array. The Coulomb blockade of the nanoparticles can be lifted by optical excitation with a laser beam. The optical excitation leads to a localized heating of the arrays, which in turn gives rise to a local change in conductance and a redistribution of the overall electrical potential in the arrays. We introduce a dual-beam optical excitation technique to probe the distribution of the electrical potential in the nanoparticle array. A negative differential photoconductance is the direct consequence of the redistribution of the electrical potential upon lifting of the Coulomb blockade. On the basis of our model, we calculate the optically induced current from the dark current-voltage characteristics of the nanoparticle array. The calculations closely reproduce the experimental observations.

Conduction Bottleneck in Silicon Nanochain Single Electron Transistors Operating at Room Temperature

Single electron transistors are fabricated on single Si nanochains, synthesised by thermal evaporation of SiO solid sources. The nanochains consist of one-dimensional arrays of ∼10 nm Si nanocrystals, separated by SiO2 regions. At 300 K, strong Coulomb staircases are seen in the drain–source current–voltage (Ids–Vds) characteristics, and single-electron oscillations are seen in the drain–source current–gate voltage (Ids–Vgs) characteristics. From 300–20 K, a large increase in the Coulomb blockade region is observed. The characteristics are explained using single-electron Monte Carlo simulation, where an inhomogeneous multiple tunnel junction represents a nanochain. Any reduction in capacitance at a nanocrystal well within the nanochain creates a conduction “bottleneck”, suppressing current at low voltage and improving the Coulomb staircase. The single-electron charging energy at such an island can be very high, ∼20kBT at 300 K.

Photon-assisted conditionality for double-dot charge qubits in a single-mode cavity

The problems of the design, control, and interaction of the single-electron double-dot charge qubits coherently coupled to the optical cavity mode are studied theoretically. A way to overcome the challenges concerned with the use of classical laser pulses for a qubit state engineering is described, replacing the lasers by a quantized photon field in a semiconductor cavity and a gate voltage. Using this strategy, a simple and efficient scheme is proposed for the creation of highly entangled multiqubit states like the nine-qubit Shor states.

Electron Counting Capacitance Standard with an improved five-junction R-pump**Official contribution of the National Institute of Standards and Technology; not subject to copyright in the United States.

The Electron Counting Capacitance Standard currently pursued at PTB aims to close the Quantum Metrological Triangle with a final precision of a few parts in 107. This paper reports the considerable progress recently achieved with a new generation of single-electron tunnelling devices. A five-junction R-pump was operated with a relative charge transfer error of five electrons in 107, and was used to successfully perform single-electron charging of a cryogenic capacitor. The preliminary result for the single-electron charge quantum has an uncertainty of less than two parts in 106 and is consistent with the value of the elementary charge.

Nonadiabatic quantum control of a semiconductor charge qubit

We demonstrate multipulse quantum control of a single electron charge qubit. The qubit is manipulated by applying nonadiabatic voltage pulses to a surface depletion gate and readout is achieved using a quantum point contact charge sensor. We observe Ramsey fringes in the excited state occupation in response to a pi/2 - pi/2 pulse sequence and extract T2* ~ 60 ps away from the charge degeneracy point. Simulations suggest these results may be extended to implement a charge-echo by reducing the interdot tunnel coupling and pulse rise time, thereby increasing the nonadiabaticity of the pulses.

Influence of confinement on single-electron charging in a network of nanoparticles

We investigated the single-electron tunneling (SET) behavior in a network of ligand stabilized Au nanoparticles (NPs) that are self-organized on an Au(111) surface by means of low-temperature scanning tunneling microscopy and spectroscopy. We demonstrate that for a proper combination of ligand chain length and NP radius the ligand shell is able to isolate a particle from the neighboring ones. This results in SET spectra with a clear Coulomb blockade and a regular staircase, similar to SET spectra obtained for isolated particles. A fraction of the investigated particles exhibits additional fine structure on top of the Coulomb charging peaks in the tunneling conductance spectra. The origin of the fine structure can be related to quantum size effects due to the very small NP size rather than to inter-particle capacitive coupling. Our findings indicate the possibility of using an individual particle in the self-organized network as the central Coulomb island in a double-barrier tunnel junction configuration, similar to the case of an isolated particle.

Single-Electron Charging in Phosphorus Donors in Silicon Observed by Low-Temperature Kelvin Probe Force Microscope

Kelvin probe force microscopy (KFM) working at low temperatures (13 K) is used to study local electronic potential fluctuations induced by individual phosphorus donors. Electronic potential maps were measured at the surface of thin phosphorus-doped channel of silicon-on-insulator field-effect transistors for different values of backgate voltage. We observed local changes of the potential profile with increasing backgate voltage, indicating electron injection in the channel. Single-step changes in the depth of the fine potential wells, observed by changing backgate voltage, are ascribed to single-electron charging in individual donors. For clusters of donors, with overlapped potential wells, electron charging occurs gradually, without single-step behavior, as the backgate voltage becomes more positive.

Single-Electron Charging in Phosphorus Donors in Silicon Observed by Low-Temperature Kelvin Probe Force Microscope

Single-Electron Charging in Phosphorus Donors in Silicon Observed by Low-Temperature Kelvin Probe Force Microscope

The effect of surface conductance on lateral gated quantum devices in Si/SiGe heterostructures

Quantum dots in Si/SiGe heterostructures are expected to have relatively long electron spin decoherence times, because of the low density of nuclear spins and the weak coupling between nuclear and electron spins. We provide experimental evidence suggesting that electron motion in a conductive layer parallel to the two-dimensional electron gas, possibly resulting from the donors used to dope the Si quantum well, is responsible for the well-known difficulty in achieving well-controlled dots in this system. Charge motion in the conductive layer can cause depletion on large length scales, making electron confinement in the dot impossible, and can give rise to noise that can overwhelm the single-electron charging signal. Results of capacitance versus gate bias measurements to characterize this conductive layer are presented.

Power loss of a single electron charge distribution confined in a quantum plasma

The dielectric tensor for a quantum plasma is derived by using a linearized quantum hydrodynamic theory. The wave functions for a nanostructure bound system have been investigated. Finally, the power loss for an oscillating charge distribution of a mixed state will be calculated, using the dielectric function formalism.

Time-resolved charge detection in graphene quantum dots

We present real-time detection measurements of electron tunneling in a graphene quantum dot. By counting single electron charging events on the dot, the tunneling process in a graphene constriction and the role of localized states are studied in detail. In the regime of low charge detector bias we see only a single time-dependent process in the tunneling rate which can be modeled using a Fermi-broadened energy distribution of the carriers in the lead. We find a non-monotonic gate dependence of the tunneling coupling attributed to the formation of localized states in the constriction. Increasing the detector bias above 2 mV results in an increase of the dot-lead transition rate related to back-action of the charge detector current on the dot.

Si/SiGe quantum dot with superconducting single-electron transistor charge sensor

We report a robust process for fabrication of surface-gated Si/SiGe quantum dots (QDs) with an integrated superconducting single-electron transistor (SSET) charge sensor. A combination of a deep mesa etch and AlOx backfill is used to reduce gate leakage. After the leakage current is suppressed, Coulomb oscillations of the QD and the current-voltage characteristics of the SSET are observed at a temperature of 0.3 K. Coupling of the SSET to the QD is confirmed by using the SSET to perform sensing of the QD charge state.

Memory Effects Based on Dopant Atoms in Nano-FETs

Transistors have been significantly downsized over the past decades, reaching channel dimensions of around 100 nm. In nanoscale, quantum effects start to play a key role in device operation, allowing the development of applications based on new physics. In silicon nanodevices, for instance, the device downsizing is associated with a reduction of the number of impurities (dopants) incorporated in the channel. Dopants can play an active role in device operation, mediating the electron transport between source and drain. Here, we present a new device concept of a memory based on the interaction between dopants in nanoscale field-effect transistors. As a basis for memory operation, we show experimental results of single-electron charging in individual dopants monitored by a single-electron current flowing through a dopant array.

Parametric Resonance in Nanoelectromechanical Single Electron Transistors

We show that the coupling between single-electron charging and mechanical motion in a nanoelectromechanical single-electron transistor can be utilized in a novel parametric actuation scheme. This scheme, which relies on a periodic modulation of the mechanical resonance frequency through an alternating source-drain voltage, leads to a parametric instability and emergence of mechanical vibrations in a limited range of modulation amplitudes. Remarkably, the frequency range where instability occurs and the maximum oscillation amplitude, depend weakly on the damping in the system. We also show that a weak parametric modulation increases the effective quality factor and amplifies the system's response to the conventional actuation that exploits an AC gate signal.

Bias-controlled single-electron charging of a self-assembled quantum dot in a two-dimensional-electron-gas-basedn−i-Schottky diode

(Received 9 December 2010; revised manuscript received 12 January 2011; published 14 February 2011) We present bias-dependent micro-photoluminescence (μ-PL) spectroscopy of the neutral (X 0 ) and singly negatively-charged (X − ) excitons in single InAs/GaAs self-assembled quantum dots (QDs) embedded in the intrinsic region of an n-i-Schottky diode based on a two-dimensional electron gas (2DEG), which was obtained from a Si δ-doped GaAs layer. Using such a device structure, we demonstrate bias-controlled single-electron charging of a single QD as the QD s-shell electron state is tuned below the Fermi level. This is verified experimentally by the sequential appearance of energetically-distinct PL emission lines from the two excitons and supported by theoretical calculations. In addition, it is shown both experimentally and theoretically that simultaneous PL emission from the X 0 and X − excitons within a particular bias range is the result of a long-lived charge-nonequilibrium state due to weak tunnel-coupling between the QDs and 2DEG in our device. Further, the ability to tune the exciton transition energies via the quantum-confined Stark effect is observed, offering insight into the carrier wave function distributions in the QD and the QD material structure. Finally, we propose a number of spintronic device concepts that may be made feasible as a result of this investigation into bias-controlled carrier tunneling between a self-assembled QD and a 2DEG.

KFM Observation of Electron Charging and Discharging in Phosphorus-Doped SOI Channel

Low temperature Kelvin Probe Force Microscopy (LT-KFM) can be used to monitor the electronic potential of individual dopants under an electric field. This capability is demonstrated for silicon-on-insulator field-effect-transistors (SOI-FETs) with a phosphorus-doped channel. We show results of the detection of individual dopants in Si by LT-KFM. Furthermore, we also observe single-electron charging in individual dopants located in the Si channel region.