Exciton Ground State Energy Research Articles

Non-polar a-plane ZnMgO/ZnO quantum wells grown by molecular beam epitaxy

Non-polar (Zn, Mg)O/ZnO quantum wells (QWs) have been grown on a r-plane sapphire by molecular beam epitaxy. The heterostructures are fully oriented and show a single wurtzite phase at least up to 40% Mg content, as evidenced by means of the x-ray pole figures analysis. The microstructure is dominated by stacking faults and related partial dislocations as shown by the transmission electron microscopy analysis. A series of QWs with different widths has then been studied, showing the absence of the quantum confined Stark effect. The photoluminescence energies of the QWs are satisfactorily simulated when taking into account the variation of the exciton binding energy with the QW width. Different approaches for the calculation of the QW exciton ground state energies are proposed and compared.

Optical emission from InAs/InP self-assembled quantum dots: evidence for As/P intermixing

We have studied the optical properties of ultrathin InAs/InP quantum wells and Stranski–Krastanov nanostructures using photoluminescence and photoluminescence excitation experiments. For InAs epilayers thinner than 2.4 monolayers, the emission spectrum consists of a single peak and the ground-state exciton energy is in good agreement with predictions based on the tight-binding method for ultrathin quantum wells. Beyond this thickness, the photoluminescence spectra evolve to a multimodal emission indicative of the presence of families of quantum dots with small heights. The emission of these quantum dots is blue-shifted significantly (∼100 meV) from the predicted values. The discrepancy is explained by As/P intermixing that occurs during quantum dot formation.

Si-SiO 2 -Si and Si-CaCO3-Si core–double-shell nanoparticles: Tuning light emission from infrared to ultraviolet

Confinement features of excitons in Si-SiO2-Si and Si-CaCO3-Si spherical nanoparticles (NPs) with a core–double-shell structure are studied in this work. In order to compute carrier and exciton ground-state energies, we estimate electron and hole effective masses in CaCO3 calcite using first-principles calculations. A comparison is made between the recombination energies and oscillator strengths of excitons in SiO2 and CaCO3 NPs as a function of diameter and barrier (middle shell) thicknesses. The recombination energy spans the energy range of the visible spectrum by changing the barrier width. The excitonic oscillator strength is orders of magnitude larger for Si-CaCO3-Si NPs in comparison to Si-SiO2-Si NPs. The results allow us to suggest that Si-CaCO3-Si nanoparticles emitting light in any wavelength between the infrared and ultraviolet can be fabricated, and are more efficient than SiO2-based ones.

Dielectric mismatch effect on the exciton states in cylindrical nanowires

The exciton ground state and excited state energies are obtained within the single band approximation for a model system of an infinitely long cylindrical wire. The effective Coulomb potential between the electron and the hole is studied as function of the wire radius and difference in dielectric permittivity inside and outside of the wire. Within the adiabatic approximation, we obtain ``exact'' numerical results for the effective exciton potential and the lowest exciton energy levels. The effective exciton potential is fitted to a tractable analytical expression that will facilitate further calculations.

Optical band gap studies on lithium aluminum silicate glasses doped with Cr3+ ions

Lithium aluminum silicate glass system (LAS) implanted with chromium ions is prepared. The reflectance and transmittance measurements are used to determine the dispersion of absorption coefficient. The optical data are explained in terms of the different oxidation states adopted by the chromium ions into the glass network. It is found that the oxidation state of the chromium depends on its concentration. Across a wide spectral range, 0.2–1.6μm, analysis of the fundamental absorption edge provides values for the average energy band gaps for allowed direct and indirect transitions. The optical absorption coefficient just below the absorption edge varies exponentially with photon energy indicating the presence of Urbach’s tail. Such tail is decreased with the increase of the chromium dopant. From the analysis of the optical absorption data, the absorption peak at ground state exciton energy, the absorption at band gap, and the free exciton binding energy are determined. The extinction coefficient data are used to determine the Fermi energy level of the studied glasses. The metallization criterion is obtained and discussed exploring the nature of the glasses. The measured IR spectra of the different glasses are used to throw some light on the optical properties of the present glasses correlating them with their structure and composition.

Effect of wetting layer on electron–hole correlation in quantum discs and rings

We propose a simple method for calculating the ground state wavefunction of anelectron–hole pair confined in a heterostructure formed by a flat quantum dotdeposited on a thin wetting layer and imbedded in a matrix made of other material.The calculations of the exciton ground state energy, the electron–hole space paircorrelation function and the density of the charge distribution have been performed forIn0.55Al0.45As–Al0.35Ga0.65As and Ga0.7Al0.3As/GaAs quantum discs and rings. It is shown that the increase of the wetting layer thickness andthe strength of the external magnetic field applied parallel to the axis lead to a lowering ofthe inner barrier height reinforcing the tunnelling of the particles into the central holeregion. We also analyse the charge distribution related to the spatial separation of theparticles due to the difference between masses of the electron and the hole. The variation ofthe quadrupole momentum sign with the increase of the ring inner radius and theappearance of the dipole momentum oriented in the crystal growth direction with theincrease of the wetting layer thickness in the presence of the electron–hole pair arepredicted.

Theoretical investigation of excitons in type-I and type-IISi∕Si1−xGexquantum wires

This work presents a theoretical study of the excitonic properties of ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ cylindrical quantum wires surrounded by a Si matrix, considering two possibilities for the conduction band alignment, type I and type II. The effect of nonabrupt interfaces between these materials on the exciton energies is investigated: an interfacial region of $15\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ in a $50\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ wide ${\mathrm{Si}}_{0.85}{\mathrm{Ge}}_{0.15}({\mathrm{Si}}_{0.7}{\mathrm{Ge}}_{0.3})$ type-I (type-II) quantum wire leads to an exciton energy blueshift of the order of $10\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. The excitonic behavior under an applied magnetic field parallel to the wire axis is also studied: exciton energies in type-I wires are weakly affected, while for type-II wires, increasing the field causes the electron angular momentum to change almost periodically, giving rise to Aharonov-Bohm oscillations of the exciton ground state energy.

Exciton states in cylindrical nanowires

The exciton ground state and excited state energies are calculated for a model systemof an infinitely long cylindrical wire. The effective Coulomb potential betweenthe electron and the hole is studied as function of the wire radius. Within theadiabatic approximation, we obtain ‘exact’ numerical results for the effectiveexciton potential and the lowest exciton energy levels which are fitted to simpleanalytical expressions. Furthermore, we investigated the influence of a magneticfield parallel to the nanowire on the effective potential and the exciton energy.

Tuning the cross-gap transition energy of a quantum dot by uniaxial stress

We show that a piezoelectric actuator can be used to apply uniaxial stress to a layer of self-assembled quantum dots. The applied stress leads to a change of the quantum dot's ground state exciton energy by up to a few hundred μ eV . This approach allows the possibility of an in situ and continuous tuning of the stress at temperatures down to 4 K and offers an alternative to tuning by temperature and Stark effect. We measure the relative change in the charging energy to the n-doped back contact by capacitance and the change in the exciton energy by photoluminescence. By tuning the uniaxial stress we are able to perform reflection spectroscopy on a single dot.

The micro-photoluminescence and micro-Raman study of Zn1－xCdx Se quantum islands (dots) in CdSe/ZnSe heterostructure

We have investigated two types of Zn1-xCdxSe quantum islands in CdSe/ZnSe heterostructure with different size and Cd composition using micro-photoluminescence and micro-Raman spectroscopy. The micro-photoluminescence spectra at 4.2 K indicate that the photoluminescence peaks of the islands have a large red-shift of 166 meV when the thickness of CdSe deposition layer increased from 1.8 ML to 2.3 ML, which can't be explained by considering the change of quantum confinement potential only. We also found two other important mechanisms which may lead to the large red-shift by comparing the micro-photoluminescence and micro-Raman spectra. First, the sheet density of large Zn1-xCdxSe islands which have lower exciton ground state energy will increase and the large islands will dominant gradually the photoluminescence properties of the samples with increasing thickness of the CdSe layer. Second, the increase of Cd composition in the Zn1-xCdxSe quantum islands contributes to the large red-shift as well. This is verified by resonant Raman scattering spectra of the samples.

Temperature dependence of the excitonic band gap inInxGa1−xAs∕GaAsself-assembled quantum dots

Single-dot spectroscopy was used to determine the temperature dependence of the ground-state exciton energy $E(T)$ in self-assembled ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}∕\mathrm{GaAs}$ quantum dots (QDs) from $T=2$ up to $\ensuremath{\sim}100\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Differences of dot composition and geometry are manifested primarily in the absolute transition energies, whereas the band-gap reduction depends only weakly on microscopic details. $E(T)$ can be well described by semiempirical phonon-dispersion models developed recently for bulk, suggesting that thermal lattice expansion and electron-phonon interaction are the dominant mechanisms for $E(T)$, whereas QD-specific mechanisms seem to be of minor importance, in contrast to observations for nanocrystals.

Exciton fractional dimension in semiconductor heterostructures arising from variational principle

We present a simple method for calculating the ground-state energy of an exciton in quantum confined structures. We express the exciton wave function as a product of the electron and hole one-particle wave functions with a variationally determined envelope function which describes the exciton intrinsic properties. Starting from the variational principle, we derive an one-dimensional wave equation for this envelope function and show that it describes a hydrogen-like atom in an effective isotropic space with the non-integer running dimension. We establish that this dimension runs from three, as the electron–hole separation is small for all heterostructures, to two in quantum well one in quantum well-wire and to zero in quantum dot, as the separation is large. The exciton ground-state energies are calculated for different confining potential shapes. Our results for GaAs-(Ga, Al)As heterostructures with square-well potential are in an excellent agreement with those obtained previously by means of other methods.

Effects of interfacial profiles on quantum levels in InxGa1−xAs/GaAs graded spherical quantum dots

A theoretical scheme describing effects of interfacial profiles on the properties of confined excitons in InxGa1 − xAs/GaAs spherical quantum dots (QDs) is presented. A two parameter variational method is used to calculate the heavy-hole and light-hole exciton energy. Our numerical results show differences in the ground state exciton energy higher than 100 meV due to gradual rather than abrupt interfaces in a 35 Å QD.

Effects of interfacial profiles on quantum levels in InxGa1 − xAs/GaAs graded spherical quantum dots

A theoretical scheme describing effects of interfacial profiles on the properties of confined excitons in InxGa1−xAs/GaAs spherical quantum dots (QDs) is presented. A two parameter variational method is used to calculate the heavy-hole and light-hole exciton energy. Our numerical results show differences in the ground state exciton energy higher than 100meV due to gradual rather than abrupt interfaces in a 35Å QD.

Optical Properties of Wurtzite GaN and ZnO Quantum Dots

AbstractWe have investigated exciton states in wurtzite GaN/AlN and ZnO quantum dots. A strong piezoelectric field in GaN/AlN quantum dots is found to tilt conduction and valence bands, thus pushing the electron to the top and the hole to the bottom of the GaN/AlN quantum dot. As a result, the exciton ground state energy in GaN/AlN quantum dots with heights larger than 3 nm exhibits a red shift with respect to bulk GaN energy gap. It is shown that the radiative decay time in GaN/AlN quantum dots is large and increases from 0.3 ns for quantum dots with height 1.5 nm to 1.1×103 ns for the quantum dots with height 4.5 nm. On the contrary, the electron and the hole are not separated in ZnO quantum dots. Moreover, a relatively thick “dead layer” is formed near the surface of ZnO quantum dots. As a result, the radiative decay time in ZnO quantum dots is small and decreases from 73 ps for quantum dots with diameter 1.5 nm to 29 ps for the quantum dots with diameter 6 nm.

Excitonic properties of strained wurtzite and zinc-blende GaN/AlxGa1−xN quantum dots

We investigate exciton states theoretically in strained GaN/AlN quantum dots with wurtzite (WZ) and zinc-blende (ZB) crystal structures, as well as strained WZ GaN/AlGaN quantum dots. We show that the strain field significantly modifies the conduction- and valence-band edges of GaN quantum dots. The piezoelectric field is found to govern excitonic properties of WZ GaN/AlN quantum dots, while it has a smaller effect on WZ GaN/AlGaN, and very little effect on ZB GaN/AlN quantum dots. As a result, the exciton ground state energy in WZ GaN/AlN quantum dots, with heights larger than 3 nm, exhibits a redshift with respect to the bulk WZ GaN energy gap. The radiative decay time of the redshifted transitions is large and increases almost exponentially from 6.6 ns for quantum dots with height 3 nm to 1100 ns for the quantum dots with height 4.5 nm. In WZ GaN/AlGaN quantum dots, both the radiative decay time and its increase with quantum-dot height are smaller than those in WZ GaN/AlN quantum dots. On the other hand, the radiative decay time in ZB GaN/AlN quantum dots is of the order of 0.3 ns, and is almost independent of the quantum-dot height. Our results are in good agreement with available experimental data and can be used to optimize GaN quantum-dot parameters for proposed optoelectronic applications.

Optical properties of confined polaronic excitons in spherical ionic quantum dots

We report the results of a variational calculation of the energy and the oscillator strength of the exciton ground state in a spherical ionic quantum dot as a function of radius, assuming infinite potential barriers. The strong interaction of the exciton with optical phonons is taken into account by using an effective potential between the electron and the hole as derived by Pollmann and B\uttner. The values of the exciton ground-state energies calculated using this effective potential are compared with the results of a recent calculation that treats the exciton interaction with confined and interface phonons independently, and excellent agreement is found. Comparisons with two simpler models of excitons reveal that the high degree of confinement in small quantum dots suppresses polaronic corrections in exciton properties. The reduction of the electron-hole correlation in small quantum dots is observed in the behavior of oscillator strength, which becomes less dependent on the form of the effective interaction as the dot size is reduced. A proper definition of exciton transition energy in ionic materials is pointed out, where self-energy renormalization effects are important. The results of our calculation are presented for quantum dots of some ionic materials such as CdSe, GaN, ZnO, and CuCl.

Excitons in quantum wires

This paper deals with excitons in quantum wires. We first study these excitons as the limit of excitons in D dimensions when $D \rightarrow 1$ . In order to do it, we have had to find a new resolution of the hydrogen atom Schrodinger equation: besides the fact that the usual resolution found in textbooks is not valid for D exactly equal to 1, it is, surprisingly enough, inconsistent since it relies on two hypergeometric functions which are not independent for the parameters of physical interest! In a second part, we write down the exact potential felt by the exciton relative motion along the wire in terms of the wire confinement. This allows a quite precise determination of the effective Coulomb potential for this 1D motion, which is of crucial importance to obtain a meaningfull finite value for the exciton ground state energy. In a last part, we study the dependence of the exciton energies on the wire area and anisotropy. While the quantitative results are here given for cylindrica l and rectangular wires with infinite barriers, we show how they can easily be extended to any particular wire shape and barrier height.

Investigation of Dynamical Parameters of Exciton Confined in CdS Spherical Quantum Dots with a B-Spline Technique**The project supported by the Doctoral Program Foundation of Institute of Higher Education of China and National Natural Science Foundation of China under Grant No. 10174098

Exciton energies as a function of radii of quantum dots in the range of 5–35 Å are calculated based on effective mass approximation model with the B-spline technique and compared with experimental and other theoretical data for the CdS dots. This method leads to accurate and fast convergent exciton energy, which are in good agreement with experimental data in the whole confinement regime. The effect of penetration of wave function from the inside to the outside of the dots and the effect of dielectric constants are taken into account. The magnitudes of dynamical parameters are discussed. It is found that the different materials surrounding the CdS quantum dot affect not only the potential energy and Coulomb interaction energy of the system, but also the effective masses. The comparison shows that the effective mass approximation model can describe very well the quantum size effects observed experimentally on the exciton ground state energy.

The polaronic shift of exciton binding energy in quantum dots with a degeneratevalence band

The polaronic shifts of the electron, hole and exciton ground state energies arestudied by taking into account the interaction between single particles and bothbulk- and interface-type LO (longitudinal optical) phonons in sphericalquantum dots with a degenerate valence band. Inclusion of the spaceconfinement effect on the phonon spectrum causes decrease of the electron,hole and exciton lowest-energy polaronic shift. The polaronic shift of theexciton energy is relatively small due to the cancellation of the polaroniceffects owing to the opposite charges of an electron and a hole. It is shownthat in the strong-confinement regime the polaronic shift of the excitonground state energy is caused by valence band degeneracy. Valence banddegeneracy also causes the ‘interface-type’ part of the hole polaronic shift.