Impurity binding energies in quantum dots with parabolic confinement

We present an effective numerical procedure to calculate the binding energies and wave functions of the hydrogen-like impurity states in a quantum dot (QD) with parabolic confinement. The unknown wave function was expressed as an expansion over one-dimensional harmonic oscillator states, which describes the electron's movement along the defined z-axis. Green's function technique used to obtain the solution of Schredinger equation for electronic states in a transverse plane. Binding energy of impurity states is defined as poles of the wave function. The dependences of the binding energy on the position of an impurity, the size of the QD and the magnetic field strength are presented and discussed.     

Polarizabilities of shallow donors in silicon

Capacitance measurements on N-type As, P, and Sb-doped Si samples have been made between 4.2 and 1.35°K, from 0.3 to 100 kHz as a function of (N_D ? N_A) [high purity to 2.7 × 10¹⁸/cm³]. From the dielectric constant variation with (N_D ? N_A) donor polarizabilities α_AS, α_P, and α_Sb are found respectively to be $\text{1.0±0.1, 2.4±0.4,}\text{and}\text{3.1±0.3 × 10}{}^5\text{A}\text{?}{}^3$.     

Polarizabilities of shallow donors in finite-barrier nanodots

Polarizabilities of shallow donors in finite-barrier GaAs/Ga_1−xAl_xAs of harmonic oscillator nanodots are calculated, within the effective-mass approximation, using the Hasse variational method. The magnetic field dependence of polarizabilities and the diamagnetic susceptibilities are computed.     

Polarizabilities of shallow donors in silicon — A comment

A recent experiment on n-type As, P and Sb-doped Si samples to study the donor polarizabilities by the capacitance measurement should be reinterpreted on the basis of the d.c. resistivity data below 4.2 K together with the concentration vs resistivity relations at room temperature.     

Three-dimensional photon confinement in a spherical microcavity with CdTe quantum dots: Raman spectroscopy

We have studied the Raman spectra of a system consisting of a polystyrene latex microsphere coated by CdTe colloidal quantum dots. The cavity-induced enhancement of the Raman scattering allows the observation of Raman spectra from only one CdTe monolayer. Periodic structure with very narrow peaks in the Raman spectra of a single microsphere was detected both in Stokes and anti-Stokes spectral regions, arising from the coupling between the emission from quantum dots and spherical cavity modes.     

A new confinement potential in spherical quantum dots: Modified Gaussian potential

A new confinement potential for spherical quantum dots, called the modified Gaussian potential (MGP), is studied. In the present work, the following problems are investigated within the effective-mass approximation: (i) the one-electron energy spectra, (ii) wave functions, (iii) the problem of existence of a bound electron state, and (iv) the binding energy of center and off-center hydrogenic donor impurities. For zero angular momentum (l=0)$(l=0)$, the new confinement potential is sufficiently flexible to obtain analytically the spectral energy and wave functions. The results obtained from the present work show that (i) the new potential is suitable for predicting the spectral energy and wave functions, and (ii) the geometrical sizes of the quantum dot play the important roles on the energy levels, wave functions, the binding energy, and the existence of a bound electron state.     

Few-electron semiconductor quantum dots with Gaussian confinement

We have performed Hartree-Fock calculations of the electronic structure of N ≤ 10 electrons in a quantum dot modeled with a confining Gaussian potential well. We discuss the conditions for the stability of N bound electrons in the system. We show that the most relevant parameter determining the number of bound electrons is V ₀ R ². Such a feature arises from widely valid scaling properties of the confining potential. Gaussian Quantum dots having N = 2, 5, and 8 electrons are particularly stable in agreement with the Hund rule. The shell structure becomes less and less noticeable as the well radius increases.      

Quantum confinement in graphene quantum dots

By performing density functional theory calculations, we studied the quantum confinement in charged graphene quantum dots (GQDs), which is found to be clearly edge and shape dependent. It is found that the excess charges have a large distribution at the edges of the GQD. The resulting energy spectrum shift is very nonuniform and hence the Coulomb diamonds in the charge stability diagram vary irregularly, in good agreement with the observed nonperiodic Coulomb blockade oscillation. We also illustrate that the level statistics of the GQDs can be described by a Gaussian distribution, as predicted for chaotic Dirac billiards.

     

Recent progresses of quantum confinement in graphene quantum dots

Graphene quantum dots (GQDs) not only have potential applications on spin qubit, but also serve as essential platforms to study the fundamental properties of Dirac fermions, such as Klein tunneling and Berry phase. By now, the study of quantum confinement in GQDs still attract much attention in condensed matter physics. In this article, we review the experimental progresses on quantum confinement in GQDs mainly by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Here, the GQDs are divided into Klein GQDs, bound-state GQDs and edge-terminated GQDs according to their different confinement strength. Based on the realization of quasi-bound states in Klein GQDs, external perpendicular magnetic field is utilized as a manipulation approach to trigger and control the novel properties by tuning Berry phase and electron–electron (e–e) interaction. The tip-induced edge-free GQDs can serve as an intuitive mean to explore the broken symmetry states at nanoscale and single-electron accuracy, which are expected to be used in studying physical properties of different two-dimensional materials. Moreover, high-spin magnetic ground states are successfully introduced in edge-terminated GQDs by designing and synthesizing triangulene zigzag nanographenes.     

A detailed investigation of the electronic properties of a multi-layer spherical quantum dot with a parabolic confinement

In this work, we aim a detailed investigation of the electronic properties of a spherical multi-layer quantum dot with and without a hydrogenic impurity. The structure is introduced in the form of core/shell/well/shell layers. The core and well layers are defined by the parabolic electronic potentials. We carry out the effect of the core radius and layer thickness on the energy levels, their wave functions, binding energies of the impurity and the probability distributions. In order to determine the sublevel eigenvalues and eigenfunctions, the Schrödinger equation is solved full numerically by shooting method in the frame of the effective mass approximation. The results are analyzed in detail as a function of the layer thicknesses and their probable physical reasons are tried to be explained. It is found that the electronic properties and impurity binding energies are strongly depending on the layer thicknesses.     

Wave-function mapping of graphene quantum dots with soft confinement

Using low-temperature scanning tunneling spectroscopy, we map the local density of states of graphene quantum dots supported on Ir(111). Because of a band gap in the projected Ir band structure around the graphene K point, the electronic properties of the QDs are dominantly graphenelike. Indeed, we compare the results favorably with tight binding calculations on the honeycomb lattice based on parameters derived from density functional theory. We find that the interaction with the substrate near the edge of the island gradually opens a gap in the Dirac cone, which implies soft-wall confinement. Interestingly, this confinement results in highly symmetric wave functions. Further influences of the substrate are given by the known moiré potential and a 10% penetration of an Ir surface resonance into the graphene layer.     

Effect of electric field and central-cell corrections on the spectrum of shallow donors in parabolic quantum wells

The effects of the electric field and of the central-corrections on the binding energies of shallow donors in a Ga As/Ga_1−x Al _x As parabolic quantum well are studied. The effectivemass approximation within a variational scheme is adopted, and central-cell corrections are calculated by using a model potential with an adjustable parameter. For great values of the parabolic parameter, relatively large corrections are obtained for the shallow donors studied.     

Temperature dependence of radiative recombination in CdSe quantum dots with enhanced confinement

We studied in details the recombination dynamics and its temperature dependence in epitaxially grown neutral CdSe/ZnSSe quantum dots with additional wide-band gap MgS barriers. Such design allows to preserve a very high quantum yield and track the radiative recombination dynamics up to room temperature. A fast initial decay of ∼0.6 ns followed by a slow decay with a time constant ∼30–50 ns is observed at low temperature T < 50 K. The fast decay gradually disappears with increasing temperature while the slow decay shortens and above 100 K predominantly a single-exponential decay is observed with a time constant ∼1.3 ns, which is weekly temperature dependent up to 300 K. To explain the experimental findings, a two-level model which includes bright and dark exciton states and a temperature dependent spin-flip between them is considered. According to the model, it is a thermal activation of the dark exciton to the bright state and its consequent radiative recombination that results in the long decay tail at low temperature. The doubling of the decay time at high temperatures manifests a thermal equilibrium between the dark and bright excitons.     

Polaronic effects in a polar semiconductor quantum strip with transverse parabolic confinement

The effect of electron–phonon interaction on the ground and excited state energies of an electron in a polar quantum strip is studied by using a variational method. It is shown that polaronic effects are quite significant and also size-dependent if the effective width of the strip is reduced below a certain value. It is also shown that the longitudinal polaron effective mass is substantially renormalized even by the transverse confinement in a quantum strip.     

Confined electron and shallow donor states in graded GaAs/Al Ga As spherical quantum dots

A theoretical study is performed on the confined electron and shallow donor states properties in graded GaAs/Al_xGa_1-xAs spherical quantum dots. The two lowest energy levels of a confined electron are obtained taking into account the dependence of the electron effective mass on the spatial profile of the Al molar fraction. The ground state of a single Si shallow donor, which may be located at an arbitrary position in the structure, is calculated through a variational approach. Depending on the dot interface width and localization, we find that the energy levels of the electron and donor states for the system under study can be blue or red shifted appreciably in comparison to those calculated within the sharp interface picture. We show that it is necessary to have accurate information concerning the interface of semiconductor dots whose samples are used in the experiments, in order to achieve a better understanding of their optical properties. Received 31 May 1999     

Experimental observation of quantum confinement in the conduction band of CdSe quantum dots

X-ray absorption spectroscopy has been used to characterize the evolution in the conduction band (CB) density of states of CdSe quantum dots (QDs) as a function of particle size. We have unambiguously witnessed the CdSe QD CB minimum (CBM) shift to higher energy with decreasing particle size, consistent with quantum confinement effects, and have directly compared our results with recent theoretical calculations. At the smallest particle size, evidence for a pinning of the CBM is presented. Our observations can be explained by considering a size-dependent change in the angular-momentum-resolved states at the CBM.     

Intraband absorption of electromagnetic radiation by quantum nanostructures with parabolic confinement potential

The intraband absorption of electromagnetic radiation by two types of nanostructures of cylindrical symmetry—by a quantum cylinder (ring) and a quantum wire—is investigated. Analytical expressions for the coefficients of absorption of high-frequency electromagnetic radiation by the electron gas of nanostructures are obtained. It is shown that the absorption curve exhibits resonance peaks and that, in the case of a degenerate gas, these peaks have breaks.