Calculation of energy levels in InGaAs/GaAs quantum dot array

The subbands of the ground state E-c1, the first excited state E-c2 and heavy hole state E-HH1 are calculated by solving the eigenvalues of effective-mass Hamiltonian H-0 which is derived from eight-band k . p theory and the calculations are performed at k(x) = k, = k = 0 for the three-dimensional array of InGaAs/GaAs quantum dots (QDs). With indium content in InGaAs QDs gradually increasing from 30% to 100%,the intersubband transition wavelength of E-c2 to E-c1, blue-shifts from 18.50 to 11.87 mu m,while the transition wavelength of E-c1, to E-HH1, red-shifts from 1. 04 to 1. 73 mu m. With the sizes of Ir-0.5 Ga-0.5 As and InAs QDs increasing from 1.0 to 5.0 nm, the intersubband transition from E-c1, to E-C2 transforms from bound-state-to-continuum-state to bound-state-to-bound-state, and the corresponding intersubband transition wavelengths red-shift from 8.12 pm (5.90 pm) to 53.47 mu m (31.87 pm), respectively, and the transition wavelengths of E-C1 to E-HH1 red-shift from 1. 13 mu m (1.60 mu m) to 1.27 mu m (2.01 mu m), respectively.

Plasmons in vertically coupled InAs/GaAs quantum dots

We investigate plasmon excitations in a quantum wire that consists of an infinite one-dimensional array of vertically coupled InAs/GaAs strained quantum dots (QDs). The research is carried out in the framework of random-phase approximation using effective-mass theory. Our formalism is capable of studying plasmons with strong tunneling among QDs, which frustrate the conventionally adopted tight-binding approximation. Based on this formalism, a systematic study on the intraminiband or intrasubband plasmon in vertically coupled InAs/GaAs strained QDs is presented. It is found that an increase of the dot spacing will inevitably reduce the plasmon energy. In contrast, the role of dot height is relatively complex and depends on the dot spacing. The results demonstrate the possibility to engineer collective excitations in low dimensional systems by simply changing their geometric configuration.

Electronic structure of Mn-doped ZnO quantum wires: A mean-field theory study

Based on the effective-mass model and the mean-field approximation, we investigate the energy levels of the electron and hole states of the Mn-doped ZnO quantum wires (x=0.0018) in the presence of the external magnetic field. It is found that either twofold degenerated electron or fourfold degenerated hole states split in the field. The splitting energy is about 100 times larger than those of undoped cases. There is a dark exciton effect when the radius R is smaller than 16.6 nm, and it is independent of the effective doped Mn concentration. The lowest state transitions split into six Zeeman components in the magnetic field, four sigma(+/-) and two pi polarized Zeeman components, their splittings depend on the Mn-doped concentration, and the order of pi and sigma(+/-) polarized Zeeman components is reversed for thin quantum wires (R < 2.3 nm) due to the quantum confinement effect.

An n-type SiGe/Ge QC structure utilizing the deep Ge quantum well for electron at the Gamma point

In this paper, an n-type Si1-xGex/Ge (x >= 0.85) quantum cascade (QC) structure utilizing a deep Ge quantum well for electrons at the Gamma point is proposed. Based on linear interpolation, a conduction band offset at the Gamma point in a Si1-xGex/Ge ( x >= 0.85) heterostructure is presented, which is suitable for designing a QC laser. This approach has the advantages of a large conduction band offset at the Gamma point, a low lattice mismatch between the Si1-xGex/Ge ( x >= 0.85) active layers and the Si1-yGey ( y > x) virtual substrate, a small electron effective mass in the Gamma band, simple conduction energy band structures and a simple phonon scattering mechanism in the Ge quantum well. The theory predicts that if high-energy electrons are continuously injected into the Gamma band, a quasi-equilibrium distribution of electrons between the Gamma and L bands can be reached and held, i.e., electrons with a certain density will be kept in the Gamma band. This result is supported by the intervalley scattering experiments. In n-type Si1-xGex/Ge ( x >= 0.85) QC structures, population inversion between the laser's upper and lower levels is demonstrated.

Electronic structures of GaAs/AlxGa1-xAs quantum double

In the framework of effective mass envelope function theory, the electronic structures of GaAs/AlxGa1-xAs quantum double rings(QDRs) are studied. Our model can be used to calculate the electronic structures of quantum wells, wires, dots, and the single ring. In calculations, the effects due to the different effective masses of electrons and holes in GaAs and AlxGa1-xAs and the valence band mixing are considered. The energy levels of electrons and holes are calculated for different shapes of QDRs. The calculated results are useful in designing and fabricating the interrelated photoelectric devices. The single electron states presented here are useful for the study of the electron correlations and the effects of magnetic fields in QDRs.

Electronic structure of ZnO wurtzite quantum wires

The electronic structure and optical properties of ZnO wurtzite quantum wires with radius R >= 3 nm are studied in the framework of six-band effective-mass envelope function theory. The hole effective-mass parameters of ZnO wurtzite material are calculated by the empirical pseudopotential method. It is found that the electron states are either two-fold or four-fold degenerate. There is a dark exciton effect when the radius R of the ZnO quantum wires is in the range of [3,19.1] nm (dark range in our model). The dark ranges of other wurtzite semiconductor quantum wires are calculated for comparison. The dark range becomes smaller when the |Delta(so)| is larger, which also happens in the quantum-dot systems. The linear polarization factor of ZnO quantum wires is larger when the temperature is higher.

Electronic structure of InSb quantum ellipsoids in an external magnetic field

The shape dependence of electronic structure, electron g factors in the presence of the external magnetic field of InSb quantum ellipsoids are investigated in the framework of eight-band effective-mass approximation. It is found that as the increasing aspect ratio e, the electron states with P character split into three doublets for the different physical interaction and the light-hole states with S character come up to the top of valence bands at e = 2.6 in comparison with the heavy-hole states. In the presence of the external magnetic field, the energy splits of electron states are different for their wave function distribution direction, and the hole ground state remain optical active for a suitable aspect ratio. The electron g factors of InSb spheres decrease with increasing radius, and have the value of about two for the smallest radius, about -47.2 for sufficiently larger radius, similar to the bulk material case. Actually, the electron g factors decrease as any one of the three dimensions increase. The more dimensions increase, the more g factors decrease. The dimensions perpendicular to the direction of the magnetic field affect the g factors more than the other dimensions. (c) 2006 Elsevier B.V. All rights reserved.

Electronic structure and g factors of CdTe quantum ellipsoids

The electronic structure, electron and hole g factors and optical properties of CdTe quantum ellipsoids are investigated, in the framework of eight-band effective-mass approximation. It is found that the light-hole states come down in comparison with the heavy-hole states when the spheres are elongated, and become the lowest states of valence band. When the aspect ratio of the ellipsoid length to diameter (e) changes from smaller than 1 to larger than 1, the linear polarization factors change from negative to positive. The electron g factors of CdTe spheres decrease with increasing radius, and are nearly 2 when the radius is very small. Actually, as some of the three dimensions increase, the electron g factors decrease. More dimensions increase, the g factors decrease. more. The dimensions perpendicular to the direction of the magnetic field affect the g factors more than the other dimension. The light-hole and heavy-hole g factors of quantum spheres are equal, and change from 0.88 to -1.14 with increasing radius. When e < 1 (e > 1) the light-hole g factor is smaller (larger) than the heavy-hole g factor. (c) 2006 Elsevier B.V. All rights reserved.

Rashba spin-orbit coupling in InSb nanowires under transverse electric field

We investigate the Rashba spin-orbit coupling brought by transverse electric field in InSb nanowires. In small k(z) (k(z) is the wave vector along the wire direction) range, the Rashba spin-orbit splitting energy has a linear relationship with k(z), so we can define a Rashba coefficient similarly to the quantum well case. We deduce some empirical formulas of the spin-orbit splitting energy and Rashba coefficient, and compare them with the effective-mass calculating results. It is interesting to find that the Rashba spin-orbit splitting energy decreases as k(z) increases when k(z) is large due to the k(z)-quadratic term in the band energy. The Rashba coefficient increases with increasing electric field, and shows a saturating trend when the electric field is large. As the radius increases, the Rashba coefficient increases at first, then decreases. The effects of magnetic fields along different directions are discussed. The case where the magnetic field is along the wire direction or the electric field direction are similar. The spin state in an energy band changes smoothly as k(z) changes. The case where the magnetic field is perpendicular to the wire direction and the electric field direction is quite different from the above two cases, the k(z)-positive and negative parts of the energy bands are not symmetrical, and the energy bands with different spins cross at a k(z)-nonzero point, where the spin splitting energy and the effective g factor are zero.

Optical properties and g factors of GaAs quantum rods

The Hamiltonian of the zinc-blende quantum rods in the framework of eight-band effective-mass approximation in the presence of external homogeneous magnetic field is given. The electronic structure, optical properties and electron g factors of GaAs quantum rods are investigated. We found that the electron g factors are very sensitively dependent on the dimensions of the quantum rods. As some of the three dimensions increase, the electron g factors decrease. The more the dimensions increase, the more the electron g factors decrease. The dimensions perpendicular to the direction of the magnetic field affect the electron g factors more than the other dimension. (c) 2006 Elsevier B.V. All rights reserved.

Electronic structure and g factors of narrow-gap zinc-blende nanowires and nanorods

The Hamiltonian in the framework of eight-band effective-mass approximation of the zinc-blende nanowires and nanorods in the presence of external homogeneous magnetic field is given in the cylindrical coordinate. The electronic structure, optical properties, magnetic energy levels, and g factors of the nanowires and nanorods are calculated. It is found that the electron states consist of many hole-state components, due to the coupling of the conduction band and valence band. For the normal bands which are monotone functions of |k(z)|, long nanorods can be modeled by the nanowires, the energy levels of the nanorods approximately equal the values of the energy band E(k(z)) of the nanowires with the same radius at a special k(z), where k(z) is the wave vector in the wire direction. Due to the coupling of the states, some of the hole energy bands of the nanowires have their highest points at k(z)=0. Especially, the highest hole state of the InSb nanowires is not at the k(z)=0 point. It is an indirect band gap. For these abnormal bands, nanorods can not be modeled by the nanowires. The energy levels of the nanorods show an interesting plait-like pattern. The linear polarization factor is zero, when the aspect ratio L/2R is smaller than 1, and increases as the length increases. The g(z) and g(x) factors as functions of the k(z), radius R and length L are calculated for the wires and rods, respectively. For the wires, the g(z) of the electron ground state increases, and the g(z) of the hole ground state decreases first, then increases with the k(z) increasing. For the rods, the g(z) and g(x) of the electron ground state decrease as the R or the L increases. The g(x) of the hole ground state decreases, the g(z) of the hole ground state increases with the L increasing. The variation of the g(z) of the wires with the k(z) is in agreement with the variation of the g(z) of the rods with the L.

Exciton states of vertically stacked self-assembled InAs quantum disks in an axial magnetic field

We have studied the exciton states of vertically stacked self-assembled quantum disks within the effective mass approximation. The ground energies of a heavy-hole and a light-hole excitons as functions of the vertical disk separation are presented and discussed. The transition energy of a heavy-hole ground-state exciton is calculated and compared with the experimental data. The binding energies are discussed in terms of the probability of ground wave function. The ground energies of a heavy-hole and a light-hole excitons as functions of the applied axial magnetic field are calculated and the effect of disk size (radius of disks) on exciton energies is discussed. (c) 2006 Elsevier B.V. All rights reserved.

Electronic states in InAs quantum spheres and ellipsoids

The eight-band effective-mass Hamiltonian of the free-standing narrow-gap InAs quantum ellipsoids is developed, and the electron and hole electronic structures as well as optical properties are calculated by using the model. The energies, wave functions and transition probabilities of quantum spheres as functions of the radius of quantum sphere R is presented. It is found that the energy levels do not vary as 1/R-2, which is caused by the coupling between the conduction and valence bands, and by the constant terms correspond to the spin-orbit splitting energy. The blueshifts of hole states depend strongly on the coupling from electron states, so that the order of hole states changes as has been predicted in experiment. The exciton binding energies are calculated, the calculated excitonic gaps as functions of the ground exciton transition energy are in good agreement with the photoluminescence measured spectra in details. Finally, the hole energy levels and the linear polarization factors in InAs quantum ellipsoids as functions of the aspect ratio are presented. The state 1S(Z up arrow)((1/2)) becomes the hole ground state when e is larger than 2.4. The saturation value of the linear polarization factors of the InAs long ellipsoids of diameter 2.0 nm is 0.86, in agreement with the experimental results.

Magneto-transport characteristics of two-dimensional electron gas for Si delta-doped InAlAs/InGaAs single quantum well

Magneto-transport measurements have been carried out on a Si heavily delta-doped In0.52Al0.48As/In(0.53)G(0.47)As single quantum well in the temperature range between 1.5 and 60 K under magnetic field up to 10 T. We studied the Shubnikov-de Haas(SdH) effect and the Hall effect for the In0.52Al0.48As/In(0.53)G(0.47)As single quantum well occupied by two subbands, and have obtained the electron concentration, mobility, effective mass and energy levels respectively. The electron concentrations of the two subbands derived from mobility spectrum combined with multi-carrier fitting analysis are well consistent with the result from the SdH oscillation. From fast Fourier transform analysis for d(2)rho/dB(2)-1/B, it is observed that there is a frequency of f(1)-f(2) insensitive to the temperature, besides the frequencies f(1), f(2) for the two subbands and the frequency doubling 2f(1), both dependent on the temperature. This is because That the electrons occupying the two different subbands almost have the same effective mass in the quantum well and the magneto-intersubband scattering between the two subbands is strong.

Electronic structures of wurtzite ZnO and ZnO/MgZnO quantum well

The band structures of wurtzite ZnO are calculated using the empirical pseudopotential method (EPM). The 8 parameters of the Zn and O atom pesudopotential form factors with Schluter's formula are obtained. The effective mass parameters are extracted by using k.p Hamiltonian to fit the EPM results. The calculated band edge energies (E-g, E-A, E-B, and E-C) at Gamma point are in good agreement with experimental results. The ordering of ZnO at the top of valence band is found to be A(Gamma(7))-B(Gamma(9))-C(Gamma(7)) due to a negative spin-orbit (SO) splitting. Based on the band parameters obtained, the valence hole subbands of wurzite ZnO/MgxZn1-xO tensile-strained quantum wells (QWs) with different well widths and Mg compositions are calculated using 6-band k.p method. (c) 2005 Elsevier B.V. All rights reserved.