Effects of magnetic field on the electronic structure of wurtzite quantum dots: Calculations using effective-mass envelope function theory

The Hamiltonian of the wurtzite quantum dots in the presence of an external homogeneous magnetic field is given. The electronic structure and optical properties are studied in the framework of effective-mass envelope function theory. The energy levels have new characteristics, such as parabolic property, antisymmtric splitting, and so on, different from the Zeeman splitting. With the crystal field splitting energy Delta(c)=25 meV, the dark excitons appear when the radius is smaller than 25.85 A in the absence of external magnetic field. This result is more consistent with the experimental results reported by Efros [Phys. Rev. B 54, 4843 (1996)]. It is found that dark excitons become bright under appropriate magnetic field depending on the radius of dots. The circular polarization factors of the optical transitions of randomly oriented dots are zero in the absence of external magnetic field and increase with the increase of magnetic field, in agreement with the experimental results. The circular polarization factors of single dots change from nearly 0 to about 1 as the orientation of the magnetic field changes from the x axis of the crystal structure to the z axis, which can be used to determine the orientation of the z axis of the crystal structure of individual dots. The antisymmetric Hamiltonian is very important to the effects of magnetic field on the circular polarization of the optical transition of quantum dots.

SEMICLASSICAL AND ENVELOPE-FUNCTION TREATMENT OF MAGNETIC LEVELS IN SUPERLATTICES UNDER AN INPLANE MAGNETIC-FIELD

The theoretical treatment of magnetic levels formed in the minibands of superlattices under an in-plane magnetic field is discussed. It is found that the results of semiclassical and envelope-function treatments based on miniband structures are in good agreement with the results calculated strictly by the quantum-mechanical method, so long as the critical parameter 2hc/eBL2 is larger than 1. The wave functions obtained are in the nature of superlattice envelope functions, which are over and above the usual effective-mass envelope functions for bulk materials.

On detection wavelength and electron-hole wave function overlap of type II InAs/In-x Ga1-x Sb superlattice infrared photodetector

In this paper, the detection wavelength and the electron-hole wave function overlap of InAs/IrxGa1-xSb type II superlattice photodetectors are numerically calculated by using the envelope function and the transfer matrix methods. The band offset is dealt with by employing the model solid theory, which already takes into account the lattice mismatch between InAs and InxGa1-xSb layers. Firstly, the detection wavelength and the wave function overlap are investigated in dependence on the InAs and InxGa1-xSb layer thicknesses, the In mole fraction, and the periodic number. The results indicate that the detection wavelength increases with increasing In mole fraction, InAs and InxGa1-xSb layer thicknesses, respectively. When increasing the periodic number, the detection wavelength first increases distinctly for small periodic numbers then increases very slightly for large period numbers. Secondly, the wave function overlap diminishes with increasing InAs and InxGa1-xSb layer thicknesses, while it enhances with increasing In mole fraction. The dependence of the wave function overlap on the periodic number shows the same trend as that of the detection wavelength on the periodic number. Moreover, for a constant detection wavelength, the wave function overlap becomes greater when the thickness ratio of the InAs over InxGa1-xSb is larger.

Size-dependent and strain rate effects in quantum dot nanostructures with molecular dynamic simulations

Size and strain rate effects are among several factors which play an important role in determining the response of nanostructures, such as their deformations, to the mechanical loadings. The mechanical deformations in nanostructure systems at finite temperatures are intrinsically dynamic processes. Most of the recent works in this context have been focused on nanowires [1, 2], but very little attention has been paid to such low dimensional nanostructures as quantum dots (QDs). In this contribution, molecular dynamics (MD) simulations with an embedded atom potential method(EAM) are carried out to analyse the size and strain rate effects in the silicon (Si) QDs, as an example. We consider various geometries of QDs such as spherical, cylindrical and cubic. We choose Si QDs as an example due to their major applications in solar cells and biosensing. The analysis has also been focused on the variation in the deformation mechanisms with the size and strain rate for Si QD embedded in a matrix of SiO2 [3] (other cases include SiN and SiC matrices).It is observed that the mechanical properties are the functions of the QD size, shape and strain rate as it is in the case for nanowires [2]. We also present the comparative study resulted from the application of different EAM potentials in particular, the Stillinger-Weber (SW) potential, the Tersoff potentials and the environment-dependent interatomic potential (EDIP) [1]. Finally, based on the stabilized structural properties we compute electronic bandstructures of our nanostructures using an envelope function approach and its finite element implementation.

Quantum Confinement Effects and Electronic Properties of SnO2 Quantum Wires and Dots

On the basis of the density functional theory (DFT) within local density approximations (LDA) approach, we calculate the band gaps for different size SnO2 quantum wire (QWs) and quantum dots (QDs). A model is proposed to passivate the surface atoms of SnO2 QWs and QDs. We find that the band gap increases between QWs and bulk evolve as Delta E-g(wire) = 1.74/d(1.20) as the effective diameter d decreases, while being Delta E-g(dot) = 2.84/d(1.26) for the QDs. Though the similar to d(1.2) scale is significantly different from similar to d(2) of the effective mass result, the ratio of band gap increases between SnO2 QWs and QDs is 0.609, very close to the effective mass prediction. We also confirm, although the LDS calculations underestimate the band gap, that they give the trend of band gap shift as much as that obtained by the hybrid functional (PBE0) with a rational mixing of 25% Fock exchange and 75% of the conventional Perdew-Burke-Ernzerhof (PBE) exchange functional for the SnO2 QWs and QDs. The relative deviation of the LDA calculated band gap difference Lambda E-g compared with the corresponding PBE0 results is only within 5%. Additionally, it is found the states of valence band maximum (VBM) and conduction band minimum (CBM) of SnO2 QWs or QDs have a mostly p- and s-like envelope function symmetry, respectively, from both LDA and PBE0 calculations.

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.

Electronic structure and optical gain of wurtzite ZnO nanowires

The electronic structure and optical gain of wurtzite ZnO nanowires are investigated in the framework of effective-mass envelope-function theory. We found that as the elliptical aspect ratio e increases to be larger than a critical value, the hole ground states may change from optically dark to optically bright. The optical gain of ZnO nanowires increases as the hole density increases. For elliptical wire with large e, the y-polarized mode gain can be several thousand cm(-1), while the x-poiarized mode gain may be 26 times smaller than the former, so they can be used as ultraviolet linearly polarized lasers. (C) 2008 American Institute of Physics.

Electronic structure of a hydrogenic acceptor impurity in semiconductor nano-structures

The electronic structure and binding energy of a hydrogenic acceptor impurity in 2, 1, and 0-dimensional semiconductor nano-structures (i.e. quantum well (QW), quantum well wire (QWW), and quantum dot (QD)) are studied in the framework of effective-mass envelope-function theory. The results show that (1) the energy levels monotonically decrease as the quantum confinement sizes increase; (2) the impurity energy levels decrease more slowly for QWWs and QDs as their sizes increase than for QWs; (3) the changes of the acceptor binding energies are very complex as the quantum confinement size increases; (4) the binding energies monotonically decrease as the acceptor moves away from the nano-structures' center; (5) as the symmetry decreases, the degeneracy is lifted, and the first binding energy level in the QD splits into two branches. Our calculated results are useful for the application of semiconductor nano-structures in electronic and photoelectric devices.

Spin-orbit splitting of a hydrogenic donor impurity in GaAs/GaAlAs quantum wells

The electronic states of a hydrogenic donor impurity in GaAs/GaAlAs quantum wells are investigated theoretically in the framework of effective-mass envelope function theory, including the effect of Rashba spin-orbit coupling. The splits of electron energy levels are calculated. The results show that (1) the split energy of the excited state is larger than that of the ground state; (2) the split energy peak appears as the GaAs well width increases from zero; and (3) the maximum split energy reaches about 1.6 meV. Our results are useful for the application of Rashba spin-orbit coupling to photoelectric devices. (c) 2008 American Institute of Physics.

Spin splitting of conduction subbands in Al0.3Ga0.7As/GaAs/AlxGa1-x As/Al0.3Ga0.7As step quantum wells

By means of the transfer matrix technique, interface-induced Rashba spin splitting of conduction subbands in Al0.3Ga0.7As/GaAs/AlxGa1-xAs/Al0.3Ga0.7As step quantum wells which contain internal structure inversion asymmetry introduced by the insertion of AlxGa1-xAs step potential is investigated theoretically in the absence of electric field and magnetic field. The dependence of spin splitting on the well width, step width and Al concentration is investigated in detail. We find that the sign of the first excited subband spin splitting changes with well width and step width, and is opposite to that of the ground subband under certain conditions. The sign and strength of the spin splitting are shown to be sensitive to the components of the envelope function at three interfaces. Copyright (C) EPLA, 2009

Linear Rashba Model of a Hydrogenic Donor Impurity in GaAs/GaAlAs Quantum Wells

The Rashba spin-orbit splitting of a hydrogenic donor impurity in GaAs/GaAlAs quantum wells is investigated theoretically in the framework of effective-mass envelope function theory. The Rashba effect near the interface between GaAs and GaAlAs is assumed to be a linear relation with the distance from the quantum well side. We find that the splitting energy of the excited state is larger and less dependent on the position of the impurity than that of the ground state. Our results are useful for the application of Rashba spin-orbit coupling to photoelectric devices.

Binding Energy and Spin-Orbit Splitting of a Hydrogenic Donor Impurity in AlGaN/GaN Triangle-Shaped Potential Quantum Well

In the framework of effective-mass envelope function theory, including the effect of Rashba spin-orbit coupling, the binding energy E-b and spin-orbit split energy Gamma of the ground state of a hydrogenic donor impurity in AlGaN/GaN triangle-shaped potential heterointerface are calculated. We find that with the electric field of the heterojunction increasing, (1) the effective width of quantum well (W) over bar decreases and (2) the binding energy increases monotonously, and in the mean time, (3) the spin-orbit split energy Gamma decreases drastically. (4) The maximum of Gamma is 1.22 meV when the electric field of heterointerface is 1 MV/cm.

Effects of shape and magnetic field on the optical properties of wurtzite quantum rods

The optical properties of quantum rods in the absence and presence of the magnetic field are studied in the framework of effective-mass envelope function theory. The two-dimensional (2D) and 1D transition dipoles of wurtzite quantum rods are investigated. It is found that the transition dipoles change from 2D to 1D as the aspect ratio of the ellipsoid increases, in agreement with the experimental results. The linear polarization factors of optical transitions of quantum rods with critical aspect ratio are zero at every orientation of the wave propagation. So quantum rods with critical aspect ratio have isotropic transition dipoles. Due to the 2D or 1D transition dipoles, the linear polarization factors of optical transitions of quantum rods change from negative or positive values to zero as the orientation of the wave propagation changes from the x axis of the crystal structure to the z axis, in agreement with the experimental results. Under magnetic field applied along the z axis of the crystal structure, the negative linear polarization factors in the 2D transition dipole case decrease as the magnetic field increases, while under magnetic field applied along the x axis, the negative linear polarization factors increase as the magnetic field increases. The antisymmetric Hamiltonian is very important to these effects of the magnetic field. It is found that quantum rods with a given radius at a given temperature have dark excitons in a range of aspect ratio. The dimensions along the x, y axes of the crystal structure play opposite roles to the dimension along the z axis on the dark exciton phenomenon. Dark excitons become bright under appropriate magnetic field.

Intersubband optical absorption in quantum dots-in-a-well heterostructures

The theoretical analysis of intersubband optical transitions for InAs/ InGaAs quantum dots-in-a-well ( DWELL ) detectors are performed in the framework of effective-mass envelope- function theory. In contrast to InAs/ GaAs quantum dot (QD) structures, the calculated band structure of DWELL quantitatively confirms that an additional InGaAs quantum well effectively lowers the ground state of InAs QDs relative to the conduction-band edge of GaAs and enhances the confinement of electrons. By changing the doping level, the dominant optical transition can occur either between the bound states in the dots or from the ground state in the dots to bound states in the well, which corresponds to the far-infrared and long-wave infrared (LWIR ) peaks in the absorption spectra, respectively. Our calculated results also show that it is convenient to tailor the operating wavelength in the LWIR atmospheric window ( 8 - 12 mu m ) by adjusting the thickness of the InGaAs layer while keeping the size of the quantum dots fixed. Theoretical predictions agree well with the available experimental data. (c) 2005 American Institute of Physics.

Asymmetric quantum-confined Stark effects of hierarchical self-assembly of GaAs/AlxGa1-xAs quantum dots

Quantum-confined Stark effects in GaAs/AlxGa1-xAs self-assembled quantum dots are investigated theoretically in the framework of effective-mass envelope function theory. The electron and hole energy levels and optical transition energies are calculated in the presence of an electric field in different directions. In our calculation, the effect of finite offset, valence-band mixing, the effects due to the different effective masses of electrons and holes in different regions, and the real quantum dot structures are all taken into account. The results show that the electron and hole energy levels and the optical transition energies can cause blueshifts when the electric field is applied along the opposite to the growth direction. Our calculated results are useful for the application of hierarchical self-assembly of GaAs/AlxGa1-xAs quantum dots to photoelectric devices. (c) 2005 American Institute of Physics.