Effective Mass Formalism Research Articles

Effect of wells thicknesses disorder on quantum magneto-transport properties in GaAs/AlxGa1-xAs multi-quantum wells near wavelength infrared detectors

We investigate theoretically, the GaAs/Al0.18Ga0.82As multi-quantum wells electronic band-structures and quantum magneto-transport properties at 1.6 ​K, using the envelope function with the effective mass formalism. The effect of well and barrier thicknesses on the band-structures and bandgap were studied. The bandgap decreases when the well thickness increases whereas an increase of barrier thickness leads to narrowing of sub-band width. The carrier’s effective masses were calculated and the electronic transport dimensionality was determinates through the density of states. The inter-plateau widths of transitions in the quantum Hall effect increases with increasing inter-layer tunneling and well thickness disorder. Our results allowed easer interpretation of quantum Hall effect measurements in the literature and are necessary for the design and engineering of multiple quantum wells infrared detectors.

Theoretical study on various contributions to the magnetization of Pb1-xEuxSe

The results of the calculation on magnetization (M) for diluted magnetic semiconductor Pb1-xEuxSe are reported. Our calculation includes two distinct contributions namely contribution from the localized magnetic impurity (Mi) and contribution from the band effect (Mb). Mi has been calculated using a three-spin cluster model which comprises the clusters consisting of one-spin (M1), two-spins (M2) and three-spins (M3). Moreover, M3 includes both open triplets (Mot) and closed triplets (Mct). The statistical distribution of the different clusters has been considered using random distribution approximation in the dilute limit. The contributions from these clusters to the magnetization have been evaluated using a modified Heisenberg's exchange Hamiltonian in the nearest approximation. The magnetization has been calculated as a function of magnetic field and impurity concentration. The band effect includes the contribution from lattice diamagnetism(χlatt). This mechanism has been considered in the effective mass formalism using a two-band k→.π→model. Our calculated values of M compare very well with experimental data where available.

Effect of size and composition on the third order nonlinear optical susceptibility for GaN/InxGa1-xN spherical core/shell quantum dot

In this report, we have theoretically described, analyzed, and investigated the nonlinear optical properties in the core/shell nanostructure of GaN core surrounded by InxGa1−xN shell. Taking in consideration the effective-mass formalism, electron eigenenergies and corresponding wave functions were calculated. Employing the compact density matrix method, highlight quantities namely the third-order nonlinear susceptibility associated with intersubband transition is numerically computed and discussed as a function of CSQD radii and indium (In) composition. Our simulations have revealed the tunability of the position and the magnitude of the resonance peaks by adjusting the geometrical parameters and the indium ratio. The magnitude of both real and imaginary parts of the susceptibility is remarkably aroused and the peaks are red shifted with the rise of core/shell radii.

Consequences of dielectric mismatch on linear and third order nonlinear optical properties for CdS/ZnSe core/shell QD-matrix

In this work, we have performed a detailed investigation on optical properties for CdS/ZnSe spherical core/shell quantum dots surrounded by various dielectric matrices such as PVA, PMMA and SiO2. The wave functions and eigenenergies of confined electrons have been theoretically computed using the effective-mass formalism and the density matrix approach. The linear and third-order nonlinear optical properties have been evaluated for different matrices. Our results demonstrated that the linear, third order nonlinear optical absorption coefficients and refractive index changes are considerably sensitive to the geometrical parameters, the incident optical intensity and the dielectric environment.

EFFECTIVE MASS KLEIN-GORDON EQUATION WITH POSITION DEPENDENT MAGNETIC FIELD

Recently, exact solutions of the classical and relativistic wave equations for the existance of an external potential have been widely studied in view of the position-dependent mass formalism. Such eorts have important applications in technology, especially in material science such as electronic properties of the semi-conductors and quantum dots. In the present study, we aim to obtain exact solutions of the Klein-Gordon equation in the presence of an exponential magnetic eld via effective mass formalism. Energy eigenvalues are derived by using wave functions. The studied magnetic eld and effective mass have the form ~B = B0e􀀀x^k and m(x) = (m0 + m1e􀀀x).

Dirac particles interacting with the improved Frost–Musulin potential within the effective mass formalism

We mainly investigate the dynamics of spin-12 particles with position-dependent mass for the improved Frost–Musulin potential under spin-pseudospin symmetry. First, we find an approximate analytical solution of the Dirac equation both for bound and scattering states under spin-pseudospin symmetry and then we see that the normalized solutions are given in terms of the Gauss hypergeometric functions. In further steps, we analyze our results numerically.

Scattering and Bound States of Klein–Gordon Particle with Hylleraas Potential Within Effective Mass Formalism

Scattering and bound states solution for the one-dimensional Klein–Gordon particle with Hylleraas potential is presented within the frame work of position dependent effective mass formalism. We calculate in detail the reflection and transmission coefficients using the properties of hypergeometric functions and the equation of continuity of the wave functions.

Density of States for Warped Energy Bands.

Warping of energy bands can affect the density of states (DOS) in ways that can be large or subtle. Despite their potential for significant practical impacts on materials properties, these effects have not been rigorously demonstrated previously. Here we rectify this using an angular effective mass formalism that we have developed. To clarify the often confusing terminology in this field, “band warping” is precisely defined as pertaining to any multivariate energy function E(k) that does not admit a second-order differential at an isolated critical point in k-space, which we clearly distinguish from band non-parabolicity. We further describe band “corrugation” as a qualitative form of band warping that increasingly deviates from being twice differentiable at an isolated critical point. These features affect the density-of-states and other parameters ascribed to band warping in various ways. We demonstrate these effects, providing explicit calculations of DOS and their effective masses for warped energy dispersions originally derived by Kittel and others. Other physical and mathematical examples are provided to demonstrate fundamental distinctions that must be drawn between DOS contributions that originate from band warping and contributions that derive from band non-parabolicity. For some non-degenerate bands in thermoelectric materials, this may have profound consequences of practical interest.

Finite-Height Effect on Electron Energy Structure of Lead Salts Nanorods

The effect of the finite height of a cylindrical lead salt nanorod on its electronic structure is studied within the effective mass formalism. It is demonstrated that, for most practical purposes, it can be accounted for by sampling the sub-band dispersion dependencies of the infinite cylindrical quantum wire of the same radius at wave numbers kz = πnz/H, where H is the nanorod height and nz is an integer. However, under certain conditions, the otherwise degenerate electron energy levels will repel. A detailed account of these conditions is provided.

Scattering of a spinless particle by an asymmetric Hulthén potential within the effective mass formalism

Effective mass Klein-Gordon equation for the asymmetric Hulthén potential is solved in terms of hypergeometric functions. Results are obtained for the scattering and bound states with the position dependent mass and constant mass, as a special case. In both cases, we derive a condition for the existence of transmission resonance (T = 1). We also study how the transmission resonance depends on the particle energy and the shape of the external potential.

On Landauer versus Boltzmann and full band versus effective mass evaluation of thermoelectric transport coefficients

Using a full band description of electronic bandstructure, the Landauer approach to diffusive transport is mathematically related to the solution of the Boltzmann transport equation, and expressions for the thermoelectric parameters in both formalisms are presented. Quantum mechanical and semiclassical techniques to obtain from a full description of the bandstructure, E(k), the density of modes in the Landauer approach or the transport distribution in the Boltzmann solution are compared and thermoelectric transport coefficients are evaluated. Several example calculations for representative bulk materials are presented and the full band results are related to the more common effective mass formalism. Finally, given a full E(k) for a crystal, a procedure to extract an accurate, effective mass level description is presented.

Electromodulation spectroscopy of In 0.53Ga 0.47As/In 0.53Ga 0.23Al 0.24As quantum wells

In 0.53Ga 0.47As/In 0.53Ga 0.23Al 0.24As quantum wells (QWs) of various widths have been grown by molecular beam epitaxy on the InP substrate and investigated by electromodulation spectroscopy, i.e. photoreflectance (PR) and contactless electroreflectance (CER). The optical transitions related to the QW barrier and the QW ground and excited states have been clearly observed in PR and CER spectra. The experimental QW transition energies have been compared with theoretical predictions based on an effective mass formalism model. A good agreement between experimental data and theoretical calculations has been observed when the conduction band offset for the In 0.53Ga 0.47As/In 0.53Ga 0.23Al 0.24As interface equals ∼60%. In addition, it has been concluded that the conduction band offset for the In 0.53Ga 0.23Al 0.24As/InP interface is close to zero. The obtained results show that InGa(Al)As alloys are very promising materials in the band gap engineering for structures grown on InP substrate.

Room temperature contactless electroreflectance of the ground and excited state transitions in Ga0.76In0.24As0.08Sb0.92∕GaSb single quantum wells of various widths

The optical transitions in Ga0.76In0.24As0.08Sb0.92∕GaSb quantum wells with the width varying from 10to21nm were studied by room temperature contactless electroreflectance (CER). In addition to the quantum well (QW) ground state transition (11H), the 22H and 33H transitions (where klH denotes transition between the kth heavy hole and the lth electron subbands) have been clearly observed in CER spectra. The experimental QW transition energies were compared with theoretical predictions based on an effective mass formalism model. It has been concluded that this QW is type I for both electron and holes and the conduction band offset for the unstrained Ga0.76In0.24As0.08Sb0.92∕GaSb interface equals ∼90%.

Ground and excited state transitions in as-grown Ga0.64In0.36N0.046As0.954 quantum wells studied by contactless electroreflectance

The optical transitions of as-grown Ga0.64In0.36N0.046As0.954 multiple quantum wells grown at the low temperature of 375°C were studied by contactless electroreflectance (CER). The investigation was carried out at room temperature for a set of samples having quantum well (QW) widths ranging from 3.9to8.1nm. The ground and the excited state transitions were clearly observed in CER spectra (the ground state transition was observed at the wavelength of 1.9μm for the 8.1nm wide QW). The experimental QW transition energies were compared with theoretical predictions based on an effective mass formalism model. Good agreement between experimental data and theoretical calculations has been obtained assuming that the conduction band offset for GaInNAs∕GaAs interface is 80% and the electron effective mass is 0.09m0.

Interband transitions inGaN0.02As0.98−xSbx∕GaAs(0<x⩽0.11)single quantum wells studied by contactless electroreflectance spectroscopy

Interband transitions in $\mathrm{Ga}{\mathrm{N}}_{0.02}{\mathrm{As}}_{0.98\ensuremath{-}x}{\mathrm{Sb}}_{x}∕\mathrm{Ga}\mathrm{As}$ single quantum wells (SQWs) with $0<x\ensuremath{\leqslant}0.11$ have been investigated by contactless electroreflectance (CER). CER features related to the ground and excited state transitions have been observed and compared with those obtained from theoretical calculations, which were performed in the framework of the effective mass formalism model. It has been concluded that these SQWs are type I and the conduction band offset for this material system decreases from 80% to 50% when the Sb composition is increased from 0% to 11%. It shows that the band gap discontinuity for $\mathrm{Ga}\mathrm{N}\mathrm{As}\mathrm{Sb}∕\mathrm{Ga}\mathrm{As}$ material system can be simply tuned by a change in Sb concentration.

Transition metal-doped quantum dots: Optical detection and manipulation of spin states

The quantum-mechanical eigenvalue problem of an exciton (electron–hole pair) in interaction with a single paramagnetic ion in a II–VI semiconductor quantum dot (QD) is studied within the multiband effective mass formalism. Initially developed for spherical nanocrystals, the model is extended to cylindrical or lower symmetries, which concern ellipsoidal and/or wurtzite nanocrystals as well as self-assembled QDs. The zero-field splitting pattern of the exciton, arising from the confinement-enhanced sp–d exchange interactions, is studied as a function of the energy separating the light- and heavy-hole-like QD valence states. The energy and polarization characteristics of the components, promising for optical detection, are calculated. We also estimate the possibility of optical manipulation of the impurity spin by a circularly polarized laser pulse.

Effective Mass Theorems for Nonlinear Schrödinger Equations

We consider time-dependent nonlinear Schrödinger equations subject to smooth lattice-periodic potentials plus additional confining potentials, slowly varying on the lattice scale. After an appropriate scaling we study the homogenization limit for vanishing lattice spacing. Assuming well-prepared initial data, the resulting effective dynamics is governed by a homogenized nonlinear Schrödinger equation with an effective mass tensor depending on the initially chosen Bloch eigenvalue. The given results rigorously justify the use of the effective mass formalism for the description of Bose--Einstein condensates on optical lattices.

Electroreflectance spectroscopy in self-assembled quantum dots: lens symmetry

Modulated electroreflectance spectroscopy $\ensuremath{\Delta}R∕R$ of semiconductor self-assembled quantum dots is investigated. The structure is modeled as dots with lens shape geometry and circular cross section. A microscopic description of the electroreflectance spectrum and optical response in terms of an external electric field $(\mathbf{F})$ and lens geometry have been considered. The field and lens symmetry dependence of all experimental parameters involved in the $\ensuremath{\Delta}R∕R$ spectrum have been considered. Using the effective mass formalism the energies and the electronic states as a function of $\mathbf{F}$ and dot parameters are calculated. Also, in the framework of the strongly confined regime general expressions for the excitonic binding energies are reported. Optical selection rules are derived in the cases of the light wave vector perpendicular and parallel to $\mathbf{F}$. Detailed calculation of the Seraphin coefficients and electroreflectance spectrum are performed for the InAs and CdSe nanostructures. Calculations show good agreement with measurements recently performed on $\mathrm{Cd}\mathrm{Se}∕\mathrm{Zn}\mathrm{Se}$ when statistical distribution on size and shape are considered, explaining the main observed characteristic in the electroreflectance spectra.

Electric-field and exciton structure in CdSe nanocrystals

Quantum Stark effect in semiconductor nanocrystals is theoretically investigated, using the effective mass formalism within a $4\times 4$ Baldereschi-Lipari Hamiltonian model for the hole states. General expressions are reported for the hole eigenfunctions at zero electric field. Electron and hole single particle energies as functions of the electric field ($\mathbf{E}_{QD}$) are reported. Stark shift and binding energy of the excitonic levels are obtained by full diagonalization of the correlated electron-hole Hamiltonian in presence of the external field. Particularly, the structure of the lower excitonic states and their symmetry properties in CdSe nanocrystals are studied. It is found that the dependence of the exciton binding energy upon the applied field is strongly reduced for small quantum dot radius. Optical selection rules for absorption and luminescence are obtained. The electric-field induced quenching of the optical spectra as a function of $\mathbf{E}_{QD}$ is studied in terms of the exciton dipole matrix element. It is predicted that photoluminescence spectra present anomalous field dependence of the emission lines. These results agree in magnitude with experimental observation and with the main features of photoluminescence experiments in nanostructures.

Confinement‐induced enhancement of spin interactions in Mn‐doped II–VI semiconductor nanocrystals

AbstractThe effects of sp–d exchange interactions on the optical properties of quantum dots containing a single Mn ion are investigated within the effective mass formalism. The quantum‐mechanical eigenvalue problem of an electron‐hole pair in interaction with the Mn spin is solved analytically. In zinc‐blende semiconductors such as CdTe the fundamental absorption line splits into six components, whose relative intensities strongly depend on the Mn spin orientation with respect to the polarization of light, suggesting the possibility of optical detection of spin. In a magnetic field the splitting between the strong components of the σ− and σ+ spectra rapidly attains a saturation value close to the overall zero‐field splitting, which is inversely proportional to the nanocrystal volume. Typically, it is an order of magnitude larger than the saturation Zeeman splitting in the corresponding bulk diluted magnetic semiconductor. The numerical results for ZnSe:Mn nanocrystals show a good agreement with the published experimental data. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)