Electronic properties of semiconductor quantum dots for Coulomb blockade applications

This paper deals with the electronic properties of Si and Ge nanocrystals (NCs) with a view to studying their potentialities for single electron devices. The 3D Poisson–Schrödinger equations are self-consistently solved for a single NC embedded in SiO₂. A 1D spherical approximation is compared to the full 3D approach. For various shapes and sizes of NC the energy levels and the density are calculated as a function of the applied voltage and the number of electrons stored in the NC. The potential properties of such nanostructures for Coulomb blockade operation are deduced.     

Coulomb blockade in molecular quantum dots

The rate-equation approach is used to describe sequential tunneling through a molecular junction in the Coulomb blockade regime. Such device is composed of molecular quantum dot (with discrete energy levels) coupled with two metallic electrodes via potential barriers. Based on this model, we calculate nonlinear transport characteristics (conductance-voltage and current-voltage dependences) and compare them with the results obtained within a self-consistent field approach. It is shown that the shape of transport characteristics is determined by the combined effect of the electronic structure of molecular quantum dots and by the Coulomb blockade. In particular, the following phenomena are discussed in detail: the suppression of the current at higher voltages, the charging-induced rectification effect, the charging-generated changes of conductance gap and the temperature-induced as well as broadening-generated smoothing of current steps.     

Lateral electron transport through single InAs quantum dots grown by molecular beam epitaxy

The transport properties of single InAs quantum dots (QDs) grown by molecular beam epitaxy have been investigated by metallic leads with nanogaps. It was found that the uncapped InAs QDs grown on the GaAs surfaces show metallic conductivities, indicating that even the exposed QDs are not depleted. On the contrary, it was found that no current flows through the exposed wetting layers. For the case of the QDs covered with GaAs capping layers, clear Coulomb gaps and Coulomb staircases have been observed at 4.2 K.     

Transport properties of quantum dots

Linear and nonlinear transport through a quantum dot that is weakly coupled to ideal quantum leads is investigated in the parameter regime where charging and geometrical quantization effects coexist. The exact eigenstates and spins of a finite number of correlated electrons confined within the dot are combined with a rate equation. The current is calculated in the regime of sequential tunneling. The analytic solution for an Anderson impurity is given. The phenomenological charging model is compared with the quantum mechanical model for interacting electrons. The current-voltage characteristics show Coulomb blockade. The excited states lead to additional fine-structure in the current voltage characteristics. Asymmetry in the coupling between the quantum dot and the leads causes asymmetry in the conductance peaks which is reversed with the bias voltage. The spin selection rules can cause a ‘spin blockade’ which decreases the current when certain excited states become involved in the transport. In two-dimensional dots, peaks in the linear conductance can be suppressed at low temperatures, when the total spins of the corresponding ground states differ by more than 1/2. In a magnetic field, an electron number parity effect due to the different spins of the many-electron ground states is predicted in addition to the vanishing of the spin blockade effect. All of the predicted features are consistent with recent experiments.     

A mean field approach to Coulomb blockade for a disordered assembly of quantum dots

The Coulomb blockade (CB) in quantum dots (QDs) is by now well documented. It has been used to guide the fabrication of single electron transistors. Even the most sophisticated techniques for synthesizing QDs (e.g. MOCVD/MBE) result in an assembly in which a certain amount of disorder is inevitable. On the other hand, theoretical approaches to CB limit themselves to an analysis of a single QD. In the present work we consider two types of disorders: (i) size disorder; e.g. QDs have a distribution of sizes which could be unimodal or bimodal in nature. (ii) Potential disorder with the confining potential assuming a variety of shapes depending on growth condition and external fields. We assume a Gaussian distribution in disorder in both size and potential and employ a simplified mean field theory. To do this we rely on the scaling laws for the CB (also termed as Hubbard U) obtained for an isolated QD [1]. We analyze the distribution in the Hubbard U as a consequence of disorder and observe that Coulomb blockade is partially suppressed by the disorder. Further, the distribution in U is a skewed Gaussian with enhanced broadening.      

In-plane and perpendicular tunneling through InAs quantum dots

A Schottky diode with InAs dots in the intrinsic GaAs region was used to investigate perpendicular tunneling (in growth direction) through InAs quantum dots (QDs). At forward bias conditions electrons tunnel from the ohmic back contact into the metal Schottky gate. Peaks appear in the differential conductance when a QD level comes into resonance with the Fermi-level of the n-doped region. The observed tunneling features are attributed to electron transport through the s- and p-shell of the InAs islands. In our in-plane tunneling experiments the islands were embedded in the channel region of an n-doped GaAs/AlGaAs HEMT-structure. In order to study tunneling through single InAs islands, a quantum point contact was defined by lithography with an atomic force microscope and subsequent wet-chemical etching. In contrast to unpatterned devices sharp peaks appear in the I–V characteristic of our samples reflecting the transport of electrons through the p-shell of a single InAs QD.     

Investigations of backscattering peaks and of the nature of the confining potential in open quantum dots

The properties of open quantum dots are examined in magneto-transport. The quantum dots are prepared from a two-dimensional electron system (2DES) in AlGaAs/GaAs by lateral gate structures. These quantum dots are open, i.e. they are still connected to the surrounding 2DES regions. The low magnetic field magnetoresistance shows peak structures. These structures can be related to semi-classical ballistic trajectories in the confining potential of a dot. The calculations of different confining potentials (abrupt “hard-wall” and parabolic “soft-wall”) are compared with the experimental results. The experiments are better described by a soft-wall potential.     

Single-electron tunneling and Coulomb blockade in carbon-based quantum dots

Single-electron tunneling (SET) and Coulomb blockade (CB) phenomena have been widely observed in nanoscaled electronics and have received intense attention around the world. In the past few years, we have studied SET in carbon nanotube fragments and fullerenes by applying the so-called “Orthodox” theory [28]. As outlined in this review article, we investigated the single-electron charging and discharging process via current-voltage characteristics, gate effect, and electronic structure-related factors. Because the investigated geometric structures are three-dimensionally confined, resulting in a discrete spectrum of energy levels resembling the property of quantum dots, we evidenced the CB and Coulomb staircases in these structures. These nanostructures are sufficiently small that introducing even a single electron is sufficient to dramatically change the transport properties as a result of the charging energy associated with this extra electron. We found that the Coulomb staircases occur in the I–V characteristics only when the width of the left barrier junction is smaller than that of the right barrier junction. In this case, the transmission coefficient of the emitter junction is larger than that of the collector junction; also, occupied levels enter the bias window, thereby enhancing the tunneling extensively.      

Optical and transport studies in coupled InAs quantum dots embedded in GaAs

We studied optical and electron transport properties of coupled InAs quantum dots (QDs) embedded in GaAs. Photoluminescence (PL) from the high dot density samples indicated asymmetry in the PL spectra when the ambient temperature is lower than about 50 K. Comparing this result with theoretical calculations, it is shown that this phenomenon is explained by the inter-dot electronic coupling effect. In the photo-conductance measurement, resonance peaks in the current–voltage characteristics were observed in the low-temperature region. The dependence of the resonance voltage on the magnetic field intensity was studied to extract the g-factor. It is also shown that the resonances are attributed to the current corresponding to the electron transport through QDs. According to these results, it is concluded that the inter-dot electronic coupling in the self-assembled InAs/GaAs QD systems occurs when the inter-dot spacing is as low as several nanometers and the ambient temperature is less than about 50 K.     

Spacing and width of Coulomb blockade peaks in a silicon quantum dot

We present an experimental study of the fluctuations of Coulomb blockade peak positions of a quantum dot. The dot is defined by patterning the two-dimensional electron gas of a silicon MOSFET structure using stacked gates. The ratio of charging energy to single-particle energy is considerably larger than in comparable GaAs/AlGaAs quantum dots. The statistical distribution of the conductance peak spacings in the Coulomb blockade regime was found to be unimodal and does not follow the Wigner surmise. The fluctuations of the spacings are much larger than the typical single-particle level spacing and thus clearly contradict the expectation of random matrix theory. Measurements of the natural line width of a set of several adjacent conductance peaks suggest that all of the peaks in the set are dominated by electrons being transported through a single-broad energy level.     

Exciton relaxation in self-assembled semiconductor quantum dots

The present study focuses on the effect of excited states on the exciton–polaron spectrum for self-assembled InAs/GaAs semiconductor quantum dots. The analytical model takes into account the Coulomb interactions between the electron and the hole as well as, each carrier, the coupling with the longitudinal optical phonon field. Furthermore, the key role played by the exciton continuum in the dot spectrum is also introduced. Such an approach is well fitted to analyze recent experimental findings about single-dot spectroscopy and allows peaks assignment, line width estimation, relaxation time evaluation, etc., necessary steps toward an understanding of the internal dynamics of quantum dots.     

Quantum phase transition and Coulomb blockade effect in triangular quantum dots with interdot capacitive and tunnel couplings

The quantum phase transition and the electronic transport in a triangular quantum dot system are investigated using the numerical renormalization group method.We concentrate on the interplay between the interdot capacitive coupling V and the interdot tunnel coupling t.For small t,three dots form a local spin doublet.As t increases,due to the competition between V and t,there exist two first-order transitions with phase sequence spin-doublet-magnetic frustration phase-orbital spin singlet.When t is absent,the evolutions of the total charge on the dots and the linear conductance are of the typical Coulomb-blockade features with increasing gate voltage.While for sufficient t,the antiferromagnetic spin correlation between dots is enhanced,and the conductance is strongly suppressed for the bonding state is almost doubly occupied.     

Single-electron transistor spectroscopy of InGaAs self-assembled quantum dots

A single-electron transistor (SET) is used to detect tunneling of single electrons into individual InGaAs self-assembled quantum dots (QDs). By using an SET with a small island area and growing QDs with a low density we are able to distinguish and measure three QDs. The bias voltage at which resonant tunneling into the dots occurs can be shifted using a surface gate electrode. From the applied voltages at which we observe electrons tunneling, we are able to measure the electron addition energies of three QDs.     

Observation of monolayer-splitting for InAs/GaAs quantum dots

A pronounced modulation is observed in the photoluminescence (PL) spectrum of self-organized InAs/GaAs quantum dots (QDs), recorded at low excitation densities. The clearly distinguishable peaks are identified as a multimodal distribution of the ground state transition energy, originating from a discrete, stepwise variation of the structural properties of the QDs, which is associated with an increase of the QD height in monolayer (ML) steps. The observation of a ML splitting implies a flat QD shape with well-defined upper and lower interfaces as well as negligible indium segregation. The electronic properties of the InAs/GaAs QDs were investigated by PL and PL-excitation spectroscopy and are discussed based on realistic calculations for flat InAs/GaAs QDs with a truncated pyramidal shape based on an extended 8-band k·p model. The calculations predict a red shift of the ground state transition with each additional ML, which saturates for heights above 9 ML, is in good agreement with experiment.     

Long-wavelength light emission from InAs quantum dots covered by GaAsSb grown on GaAs substrates

We fabricated InAs quantum dots (QDs) with a GaAsSb strain-reducing layer (SRL) on a GaAs(0 0 1) substrate. The wavelength of emission from InAs QD is shown to be controllable by changing the composition and thickness of the SRL. An increase in photoluminescence intensity with increasing compositions of Sb and thickness of the GaAsSb SRL is also seen. The efficiency of radiative recombination was improved under both conditions because the InAs/GaAsSb/GaAs hetero-interface band structure more effectively suppressed carrier escape from the InAs QDs.     

Selective excitation of self-assembled quantum dots by using shaped pulse

We carried out optical selective excitation of individual self-assembled quantum dots by using phase-modulated pulses. Based on scattered photoluminescence excitation resonances in individual QDs, the excitation pulses modulated in the spectral region allows for addressing individual ground states emission. The photoluminescence spectra including several QDs showed intensity changes according to both the modulation energies and phases. The results also suggested the individual control of selective QDs even in collective excitation.     

Growth and optical characterization of dense arrays of site-controlled quantum dots grown in inverted pyramids

We report on the growth and optical properties of dense arrays of single GaAs/AlGaAs quantum dot (QD) heterostructures with pitches as small as 300 nm. The samples were grown by organometallic chemical vapor deposition in dense inverted pyramids on {1 1 1}B GaAs substrate pre-patterned using electron beam lithography and wet chemical etching. The growth conditions such as deoxidation and growth temperatures, growth rates, and V/III ratio, had to be chosen quite differently from those employed with micron-size pyramids. Low-temperature micro-photoluminescence and cathodoluminescence spectra of the samples show distinct luminescence from the QDs with a linewidth of less than 1 meV and uniform emission energy for an ensemble of 900 QDs. The possibility of incorporating such QD arrays inside optical microcavity structures is also discussed.     

Analysis of inelastic scattering processes of electrons by localized electrons in quantum dots

The inelastic Coulomb scattering rate 1/τ_in of conduction electrons has been theoretically evaluated in the presence of localized states such as quantum dots. By a diagrammatical method, we have formulated 1/τ_in and its relation to the conductivity σ_loc(ω) through localized states. The dependence of τ_in on temperature T is examined in the case that σ_loc(ω) follows the Mott's model. It is found that 1/τ_in varies as T²(ln Δ/T)^d+1 where d is the dimensionality and Δ is tunneling energy between the localized states in the asymptonic T = 0 limit, in agreement with Imry's calculation. It is also found that calculated 1/τ_in deviates from T²(ln Δ/T)^d+1 as T increases, suggesting the importance of correction term at high temperature.     

Nano-probe-assisted technology of indium-nano-dot formation for site-controlled InAs/GaAs quantum dots

We have successfully and reproducibly fabricated uniform indium (In) nano-dots at a selected point. Nano-dot formation was realized using an atomic force microscope (AFM) probe with a specially designed cantilever, which was equipped with a hollow pyramidal tip with a sub-micron size aperture on the apex and an In-reservoir tank within the stylus. The In nano-dots formed in this study can be directly converted to InAs quantum dots by subsequent irradiation of arsenic flux in the molecular beam epitaxy chamber, which is connected to the AFM chamber through an ultra-high-vacuum tunnel.     

Tunable quantum dot resonator embedded in a quantum wire

Combined quantum wire and quantum dot system is theoretically predicted to show unique conductance properties associated with Coulomb interactions. We use a split gate technique to fabricate a quantum wire containing a quantum dot with two tunable potential barriers in a two-dimensional electron gas. We observe the effects of the quantum dot cavity on the electron transport through the quantum wire, such as Coulomb oscillations near the pinch-off voltage and periodic conductance oscillations on the first conductance plateau.