Energy Levels Of Quantum Dots Research Articles

Carrier‐carrier and carrier‐phonon scattering in the low‐density and low‐temperature regime for resonantly pumped semiconductor quantum dots

AbstractWe study carrier relaxation due to Coulomb scattering and interaction with LO‐phonons in semiconductor quantum dots at low temperatures. Scattering for different relaxation process are evaluated for various carrier distributions that correspond to stages of the typical relaxation kinetics after optical excitation with a weak pulse, generating on average less than one electron per quantum dot.Even when the spacing of the quantum dot energy levels does not match the LO‐phonon energy, we.nd that carrier‐LO‐phonon scattering, in addition to electronelectron and electron‐hole interaction, provides efficient carrier relaxation. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Intermixing of InAs/GaAs quantum dots by proton implantation and rapid thermal annealing

Low-temperature photoluminescence (PL) experiments have been carried out to investigate In/Ga intermixing in InAs/GaAs self-assembled quantum dots (QDs) by studying the changes in the optical properties of the system by rapid thermal annealing (RTA) and by room temperature proton implantation at various doses followed by RTA. The study of the RTA effect on the investigated structure shows that thermal stability can be ensured for an annealing temperature below 675 °C. For higher annealing temperatures, the thermal intermixing is found to change both the optical transition energy and the inter-sublevel spacing of the QD energy levels. By using proton implantation at various doses and subsequent annealing at 675 °C for 30 s, a tunable energy shift up to 130 meV has been obtained. The band gap tuning limit for this system has been achieved for an implantation dose of 5×10 13 cm −2. Regardless of the intermixing technique employed, a pronounced PL peak broadening is found to occur at low annealing temperatures and/or proton implantation doses.

Energy levels of a spherical quantum dot in a confining potential

Using an exact analytical method, we obtain the ground state and the excited states wave functions as well as the corresponding eigenvalues of a spherical quantum dot in the presence of a confining potential which is a combination of linear, Coulomb and quadratic terms. Next, we investigate the quantum dot energy as the potential coefficients are changed. Our study reveals that considering such a confining potential leads to results which are in good agreement with experimental results.

Fano effect in a Josephson junction with a quantum dot

We theoretically investigate the Fano effect in dc Josephson current at the absolute zero of temperature. The system under consideration is a double-path Josephson junction in which one path is through an insulating barrier and the other one is through a quantum dot (QD). Here the Kondo temperature is assumed to be much smaller than the superconducting gap, and the Coulomb interaction inside the QD is treated by the Hartree-Fock approximation. It is shown that the Josephson critical current exhibits an asymmetric resonance against the QD energy level. This behavior is caused by the interference between the two tunneling processes between the superconductors: the direct tunneling across the insulating barrier and the resonant one through the QD. Moreover, we find that the Josephson critical current changes its sign around the resonance when the Coulomb interaction is sufficiently strong. Our results suggest that $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition is induced by the cooperation of the Fano effect and the Coulomb interaction inside the QD.

Improving size distribution of InAs quantum dots for intersubband devices

We present the growth and characterization of InAs quantum dots on Al x Ga 1− x As surfaces for intersubband devices. This requires the quantum dot energy levels in the Al x Ga 1− x As matrix to be above the GaAs bandedge. Using standard As 4 fluxes (beam equivalent pressure 8e−6 Torr), inhomogeneous broadening of the quantum dot size distribution increases with increasing Al content in the Al x Ga 1− x As matrix. Reducing the As 4 overpressure during In deposition is found to greatly improve the size distribution of the quantum dots, while producing slightly larger dots and a reduction in the density of small dots ( h<1.3 nm). Annealing at the higher standard As 4 flux for 30 s, after the reduced As 4 In deposition, produced a negligible change in the quantum dot size distribution. Utilizing surface dots on top of 30 layers of self-assembled quantum dots, the maximum quantum dot height for ground state energies above the GaAs bandedge is determined to be 2 nm for Al 0.30Ga 0.7As and 3 nm for Al 0.45Ga 0.55As.

Josephson current transport through T-shaped double quantum dots

The Josephson current through T-shaped double quantum dots (TDQD) has beeninvestigated theoretically using the non-equilibrium Green’s function method.Hybridization of energy levels of the central quantum dot (QD) and side QDresults in the renormalization of Andreev bound states, which dominates theJosephson current. Consequently, Josephson critical current can be modulated tointerference construction and destruction by adjusting the energy levels of two QDsε1,ε2, and interdotcoupling tc. Indetail, when ε1ε2 = tc2 is fulfilled, interference construction occurs and whenε2 = 0, interference destruction happens. These results are similar to the interferencebehavior of linear conductance in normal TDQD devices. In addition,Josephson critical current also shows Fano characteristics with variation ofε2 and the resonance line shape is determined byε1. Finally, the Josephson current has a symmetric relation ofI(ε1,ε2) = I(−ε1,−ε2) due to electron–hole symmetry.

Parabolic band approximation of the electron energy levels in a tetrahedral-shaped quantum dot

In more elaborate schemes, an electron’s effective mass in a heterostructure semiconductor quantum dot (QD) depends on both its position and its energy. However, the electron’s effective mass can be simply modeled by a parabolic band approximation — the electron’s effective mass inside the QD — which is assumed to be constant and differs from the one outside the QD, which is also assumed to be constant. The governing equation to be solved for the electron’s energy levels inside the QD is the nonlinear Schrödinger equation. With the approximation, the nonlinear Schrödinger equation for a tetrahedral-shaped QD is discretized by using the finite-volume method. The discretized nonlinear Schrödinger equation is solved for the electron energy levels by a computer program. It is noted that the resulting energy levels for the parabolic mass model are nondegenerate due to the mass-gradient term at the corners, edges, and surfaces of the tetrahedral-shaped QD.PACS Nos.: 02.60.Cb, 03.65.Ge, 81.07.Ta

Effects of Shape and Strain Distribution of Quantum Dots on Optical Transition in the Quantum Dot Infrared Photodetectors

We present a systemic theoretical study of the electronic properties of the quantum dots inserted in quantum dot infrared photodetectors (QDIPs). The strain distribution of three different shaped quantum dots (QDs) with a same ratio of the base to the vertical aspect is calculated by using the short-range valence-force-field (VFF) approach. The calculated results show that the hydrostatic strain ɛHvaries little with change of the shape, while the biaxial strain ɛBchanges a lot for different shapes of QDs. The recursion method is used to calculate the energy levels of the bound states in QDs. Compared with the strain, the shape plays a key role in the difference of electronic bound energy levels. The numerical results show that the deference of bound energy levels of lenslike InAs QD matches well with the experimental results. Moreover, the pyramid-shaped QD has the greatest difference from the measured experimental data.

Scanning Tunnelling Spectroscopy on Arrays of CdSe Quantum Dots: Response of Wave Functions to Local Electric Fields

We use scanning tunnelling microscopy (STM) to controllably contact individual CdSe quantum dots (QDs) in a multilayer array to study electrical contacts to a model QD solid. The probability of electron injection into the QD array depends strongly on the symmetry of the QD wave functions and their response to the local electric field. Quantitative spectroscopy of the QD energy levels is possible if the potential distribution in the STM tip-QD array-substrate system is taken into account.

Spin polarization in parallel double dots with spin–orbit interaction

Spin polarization in parallel double quantum dots embedded in arms of Aharonov–Bohm interferometer is investigated. The spin–orbit interaction exists in quantum dots. We find that the spin polarization is quite large even with a weak spin–orbit interaction. The direction and the strength of the spin polarization are well controllable and manipulatable by simply varying the strength of spin–orbit interaction or the energy levels in quantum dots. Moreover, electron–electron interaction strengthens the spin accumulation when the energy levels of the two quantum dots are identical. As the energy levels are unequal, electron–electron interaction cannot increase the spin accumulation. It is worth mentioning that the device is free of a magnetic field or a ferromagnetic material and it can be easily realized with present technology.

Effect of ZnS shell formation on the confined energy levels of ZnSe quantum dots

Photoluminescence excitation spectroscopy was employed to investigate the electronic structure of ZnSe/ZnS core/shell quantum dots. Four excited states viz. $1{S}^{e}\ensuremath{-}1{S}_{3/2}^{h}$, $1{S}^{e}\ensuremath{-}2{S}_{3/2}^{h}$, $1{P}^{e}\ensuremath{-}1{P}_{3/2}^{h}$, and $1{S}^{e}\ensuremath{-}1{S}^{SO}$ are observed in ZnSe and ZnSe/ZnS core/shell quantum dots. The experimentally observed excited states for ZnSe/ZnS quantum dots are analyzed on the basis of reported ``effective mass approximation'' calculations. The photoluminescence quantum efficiency increased from 2% for ZnSe quantum dots to 42% for ZnSe/ZnS quantum dots. X-ray photoelectron spectroscopic and transmission electron microscopic investigations suggest formation of uniform ZnS shell on ZnSe. The electron energy levels of ZnSe/ZnS core/shell quantum dots are investigated as a function of core diameter and ZnS shell thickness, and are compared with bare ZnSe quantum dots. Seven different sizes (ranging between 20 to $52\text{ }\text{\AA{}}$) are probed using size-selective photoluminescence excitation technique. Upon building a shell of ZnS on ZnSe quantum dots, the transition from three hole states ($1{S}_{3/2}^{h}$, $2{S}_{3/2}^{h}$, $1{S}^{SO}$) to $1{S}^{e}$ remain well defined and have negligible relative shift, suggesting that the valence-band offset is larger than the energy of these states. With increasing ZnS shell thickness, an observed increase in the transition probability of $1{S}^{e}\ensuremath{-}2{S}_{3/2}^{h}$ state is due to modification of hole states caused by ZnS shell. The relative shift of the $P$ exciton peak $(1{P}^{e}\ensuremath{-}1{P}_{3/2}^{h})$ with increase in shell thickness is due to a loss of confinement energy of $P$ electron state. The energy of $1{P}^{e}\ensuremath{-}1{P}_{3/2}^{h}$ is found to be remarkably independent as a function of core diameter.

Modulation of single quantum dot energy levels by a surface-acoustic-wave

This letter presents an experimental investigation into the effect of a surface-acoustic-wave (SAW) on the emission of a single InAs quantum dot. The SAW causes the energy of the transitions within the dot to oscillate at the frequency of the SAW, producing a characteristic broadening of the emission lines in their time-averaged spectra. This periodic tuning of the transition energy is used as a method to regulate the output of a device containing a single quantum dot and we study the system as a high-frequency periodic source of single photons.

Electronic Energy Levels in an Asymmetric Quantum-Dots-in-a-Well Structure for Infrared Photodetectors

Theoretical calculation of electronic energy levels of an asymmetric InAs/InGaAs/GaAs quantum-dots-in-a-well (DWELL) structure for infrared photodetectors is performed in the framework of effective-mass envelope-function theory Our calculated results show that the electronic energy levels in quantum dots (QDs) increase when the asymmetry increases and the ground state energy increases faster than the excited state energies. Furthermore, the results also show that the electronic energy levels in QDs decrease as the size of QDs and the width of quantum well (QW) in the asymmetric DWELL structure increase. Additionally, the effects of asymmetry, the size of QDs and the width of QW on the response peak of asymmetry DWELL photodetectors are also discussed.

Electron dynamics in the coupled double quantum dots system

We have studied the electron dynamics in different geometrical arrangements of the two coupled double quantum dot structures. Applying the equation of motion method for appropriate correlation functions the occupation probabilities of different quantum dots of the considered system has been theoretically investigated. The numerical calculations were performed for different forms of the time-dependent tunneling amplitudes and quantum dot energy levels. We found, among others, that under some conditions for the tunneling amplitudes changed in the form of Gaussian pulses it is possible to localize the electron in a controlled manner on the given dot of the considered system.

Near‐field control of the light emission properties of a symmetric semiconductor quantum dot

AbstractWe study the carrier capture and distribution among the available energy levels of a symmetric semiconductor quantum dot under continuous‐wave optical excitation resonant with the barrier energy levels. We find that at low temperature all the dot level‐occupations but one decrease monotonically with energy. The uncovered exception, corresponding to the second (dark) energy level, displays a steady‐state carrier density exceeding that of the lowest level more than a factor two. The root cause is not radiative recombination before relaxation to lower energy levels, but at the opposite, carrier trapping due to the symmetry‐induced suppression of radiative recombination. We show that spatially resolved photoluminescence spectroscopy can detect the evanescent waves generated by dark states occupations, allowing the observation of such effects. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Near-field light emission from dark states excitonic occupations

We theoretically analyze the carrier capture and distribution among the available energy levels of a symmetric semiconductor quantum dot under continuous-wave excitation resonant with the barrier energy levels. At low temperature, all the dot level occupations but one monotonically decrease with energy. The uncovered exception, corresponding to the second (dark) energy level, displays a carrier density exceeding that of the lowest level by more than a factor two. The root cause is not radiative recombination before relaxation, but instead, carrier trapping due to the symmetry-induced suppression of radiative recombination. Such a behavior can be observed by collection-mode near-field optical microscopy.

Theoretical investigations of transport through a Kondo dot with a side-coupled noninteracting quantum-dot array

Based on the slave boson approach and the Keldysh Green’s function technique, we investigate theoretically the transport properties of a mesoscopic structure consisting of a Kondo quantum dot with a side-coupled noninteracting quantum-dot array at zero temperature, in which only the Kondo dot is coupled to the leads. When the interdot coupling strengths inside the sided-coupled noninteracting quantum-dot array are compared with the Kondo temperature of the single Kondo dot, the local density of states (LDOS) may be decomposed into one Breit–Wigner and multiple Fano line shapes due to the Fano–Kondo interactions when the appropriate system parameters are considered. The odd–even parity of the linear conductance is also found with the number of side-coupled quantum dots in the array changing, in which the energy levels of quantum dots are pinned at the Fermi energy in the leads. The odd–even parity is broken when the energy levels of side-coupled quantum dots in the quantum array depart from the Fermi energy.

Pauli-spin-blockade transport through a silicon double quantum dot

We present measurements of resonant tunneling through discrete energy levels of a silicon double quantum dot formed in a thin silicon-on-insulator layer. In the absence of piezoelectric phonon coupling, spontaneous phonon emission with deformation-potential coupling accounts for inelastic tunneling through the ground states of the two dots. Such transport measurements enable us to observe a Pauli spin blockade due to effective two-electron spin-triplet correlations, evident in a distinct bias-polarity dependence of resonant tunneling through the ground states. The blockade is lifted by the excited-state resonance by virtue of efficient phonon emission between the ground states. Our experiment demonstrates considerable potential for investigating silicon-based spin dynamics and spin-based quantum information processing.

Near‐field light emission from dark‐states in semiconductor quantum dots

AbstractWe theoretically study the carrier capture and distribution among the available energy levels of a symmetric semiconductor quantum dot under continuous‐wave excitation resonant with the barrier energy levels. We find that at low temperature all the dot level‐occupations but one, the second (dark) energy level,decrease monotonically with energy. The second energy level, displays a steady‐state carrier density exceeding that of the lowest level more than a factor two (see the figure). This nonequilibrium effect does not origin from radiative recombination before relaxation to lower energy levels, but at the opposite, it is consequence of carrier trapping due to the symmetry‐induced suppression of radiative recombination of the second (dark) energy level. While the observation of such effect by means of far‐field spectroscopy is prevented, scanning near‐field optical microscopy, able to detect the evanescent waves generated by dark‐states occupations, can be adopted to inspect such nonequilibrium effects at the nanoscale. Exciton‐level occupations of the dot (normalized at the maximum) calculated for two different temperatures. See Sect. 3 for a detailed description of the results here displayed. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Electron energy level statistics in graphene quantum dots

Motivated by recent experimental observations of size quantization of electron energy levels in graphene quantum dots \cite{ponomarenko} we investigate the level statistics in the simplest tight-binding model for different dot shapes by computer simulation. The results are in a reasonable agreement with the experiment which confirms qualitatively interpretation of observed level statistics in terms of "Dirac billiards" without taking into account many-body effects. It is shown that edge effects are in general sufficient to produce the observed level distribution and that even strong bulk disorder does not change the results drastically.