Electron–hole transition in a spherical quantum dot confined at the center of a cylindrical nano-wire: Comparison of isotropic and anisotropic effective mass

Electronic structure of an InAs spherical quantum dot placed at the center of a GaAs cylindrical nano-wire is investigated. The Schrodinger equation within the effective mass approximation is solved and the energy eigenvalues and transition energies are calculated as a function of quantum dot and nano-wire radii using the finite element method. The two types of heavy holes, hhI and hhII, with isotropic and anisotropic effective masses are considered, respectively. The effect of spherical and nano-wire confining potentials, the size of the dot and the nano-wire on ground and first excited state energies of the electron, heavy hole I and heavy hole II are investigated. The results show that the electron and heavy holes energies decrease as the dot and the nano-wire radii increase. The emitted wavelength of transitions between el-hhI and el-hhII are also calculated and compared. The results show that the anisotropy of the effective mass has great effect on the emitted wavelength.     

Hydrostatic pressure and temperature effects on the electronic energy levels of a spherical quantum dot placed at the center of a nano-wire

The effect of pressure and temperature on the electronic structure of an InAs spherical quantum dot located at the center of a GaAs cylindrical nano-wire have been determined using finite element method, within the effective mass approximation. The energy levels and transition energies are numerically calculated as a function of the dot radius, pressure and temperature. It is shown that the pressure and temperature effects are significant and should be considered in the study of low-dimensional semiconducting systems. The results show that; energy levels (i) decrease as the dot radius increases (ii) decrease as the pressure increases and (iii) increase as the temperature increases. For very small dot radii, the energy levels show unusual behavior, such that the energy levels increase as the pressure increases. We also found that the transition energy (i) increases as the dot size decreases (ii) increases as the pressure increases and (iii) decreases as the temperature increases.     

Finite-difference calculation of donor energy levels in a spherical quantum dot subject to a magnetic field

The ground and excited states of a donor impurity at the center of a spherical quantum dot subject to a magnetic field are calculated within the effective-mass approximation. The barriers are infinitely high and the differential equation is solved by combining the finite-difference method with the Richardson extrapolation. The binding and transition energies are more accurate than the available variational values, and excellent agreement is found with the hydrogen atom. The transition energies for a medium-size quantum dot are given.     

Binding energy and diamagnetic susceptibility of an on-center hydrogenic donor impurity in a spherical quantum dot placed at the center of a cylindrical nano-wire

The binding energy and diamagnetic susceptibility of an on-center hydrogenic donor impurity in an InAs spherical quantum dot placed at the center of a GaAs cylindrical nano-wire have been investigated using finite element method in the framework of the effective mass approximation. The binding energy and diamagnetic susceptibility are calculated as a function of the dot radius, nano-wire radius and nano-wire height. The results show that as the dot radius increases (I) for a dot radius smaller than some critical value, the effect of the spherical confinement on the energy levels becomes negligible and the energies remain constant, for a dot radius larger than some specific value, the energy levels decrease (II) the ground and the first excited state binding energies increase, reach a maximum and then decrease (III) the ground state diamagnetic susceptibility increases, reach a maximum and then decreases (IV) the first excited state diamagnetic susceptibility increases, indicating two maxima and then decreases. The effects of the nano-wire dimensions on the binding energy and diamagnetic susceptibility have also been studied. We found that the binding energy and diamagnetic susceptibility decrease reach a minimum value and then increase as the nano-wire radius increases. Finally we found that as the height of the nano-wire increases the ground state binding energy decreases, reaches a minimum value and then increases but the first excited state binding energy decreases and reaches a constant value.     

纤锌矿GaN/AlxGa1-xN应变柱形量子点中杂质态结合能及其压力效应

考虑应变及流体静压力,在有效质量近似下,利用变分法计算了无限高GaN/Al<,x>Ga<,1-x>N应变柱形量子点中类氢杂质结合能.结果表明,在量子点尺寸较小情况下,应变增加了杂质态结合能;而在量子点尺寸较大情况下,应变降低了杂质态结合能.随着Al摩尔分数的增加,杂质态结合能减小.杂质态结合能随着流体静压力的增加而增大...     

透镜型量子点中类氢杂质基态能的计算

通过有效质量近似和变分法，研究了垂直磁场下透镜型量子点中类氢杂质基态能量，并与球型量子点进行了比较.研究表明：对于球型量子点，基态能仅与杂质的偏离距离有关，与垂直和水平偏离无关；而对于透镜型量子点，由于水平方向和垂直方向束缚势的非对称性，电子基态能不仅与杂质的偏离距离有关，还与杂质偏离方向有关. 关键词： 透镜型量子点 基态能 变分法     

Double donor in a spherical quantum dot

We present a variational calculation for the ground state of the double donor in a spherical GaAs–Ga_1–x Al _x As quantum dot. The binding energies for the ionized and neutral centres are calculated for several barrier height values as a function of the radius of the dot. Compared with a square well structure, there is a stronger confinement and a larger binding energy for the double donors in a spherical quantum dot.     

Effects of Electric Field on Electronic States in a GaAs/GaAlAs Quantum Dot with Different Confinements

Binding energies of shallow hydrogenic impurity in a GaAs/GaAlAs quantum dot with spherical confinement, parabolic confinement and rectangular confinement are calculated as a function of dot radius in the influence of electric field. The binding energy is calculated following a variational procedure within the effective mass approximation along with the spatial depended dielectric function. A finite confining potential well with depth is determined by the discontinuity of the band gap in the quantum dot and the cladding. It is found that the contribution of spatially dependent screening effects are small for a donor impurity and it is concluded that the rectangulax confinement is better than the parabolic and spherical confinements. These results are compared with the existing literature.     

压力下GaN/Ga1-xAlxN量子点中杂质态的界面效应

考虑界面处导带弯曲,流体静压力以及有效质量随量子点位置的依赖性,采用变分法以及简化相干势近似,研究了无限高势垒GaN/Ga_1-xAl_xN球形量子点中杂质态的界面效应,计算了杂质态结合能随量子点尺寸、电子面密度以及压力的变化关系。结果表明,结合能随压力的增大呈线性增加的趋势,有效质量位置的依赖性以及导带弯曲对结合能有不容忽视的影响。     

Binding energy of a screened donor in a spherical quantum dot with a parabolic potential

A wavefunction is proposed for calculating the ground-state energy of a screened donor in a spherical quantum dot under a parabolic potential by a variational method. The donor is taken to be at the center of the quantum dot. Results are presented for four values of the screening parameter by the proposed wavefunction as well as for the hydrogenic donor case by a wavefunction used by Xiao et al.. To assess the accuracy of the results, ‘exact’ energies are also obtained by numerical integration of the Schrödinger equation. It is shown that the proposed wavefunction gives very good results in all cases including the hydrogenic donor case.     

Effect of an intense laser field on donor impurities in spherical quantum dots

The effect of an intense laser field on the binding energy of hydrogenic impurity states with an impurity atom located at the center of a spherical quantum dot confined by an infinite barrier potential are studied as a function of the dot radius and of the intensity and frequency of the laser field. Accurate binding energies are obtained for the 1s, 2s and 2p states by numerical integration of the Schrödinger equation. The binding energies are found to increase with decrease in the dot radius, and decrease with increase in the value of the laser field amplitude λ in all cases.     

Influence of the image charge effect on the hydrogen-like impurity-bound polaron in a spherical quantum dot in the presence of an electric field

We have investigated the influence of an external electric field on the binding energies and polaronic shifts of the ground and some first few excited states of a hydrogenic impurity in a spherical quantum dot by taking into account the image charge effect. By using Landau–Pekar variational method the general analytical expression is obtained for the impurity bound-polaron energies. It has been numerically identified the conditions (electric field, nominal radius of quantum dot, etc.) in which the bound-polaron states can be existence in GaAs quantum dot. We have shown that the polaronic shifts in the binding energy of 1s-like state are the same in cases with and without image charge effect while they for 2s-like state are not coincide and have different monotonic behavior versus confinement potential. Electron–phonon interaction lifts the degeneracy of the 2px-, 2py-, and 2pz-like states of a donor impurity and reduces their binding energies.     

Simultaneous effects of pressure and temperature on the binding energy and diamagnetic susceptibility of a laser dressed donor in a spherical quantum dot

Binding energies and diamagnetic susceptibility of an impurity in a spherical GaAs quantum dot under the simultaneous influence of static pressure, temperature and laser radiation are investigated. Pressure- and temperature-dependent dressed potential which is produced by the combined effects of laser radiation and impurity considerably change the energy spectrum and diamagnetic susceptibility of the system. It is shown that binding energies and diamagnetic susceptibility increase with increasing pressure. Moreover, laser radiation effects on the diamagnetic susceptibility are not significant in comparison with its effects on the binding energy.     

Pressure-induced threshold optical pump intensity in a CdTe/ZnTe quantum dot

Pressure-induced binding energies of an exciton and a biexciton are studied taking into account the geometrical confinement effect in a CdTe/ZnTe quantum dot. Coulomb interaction energy is obtained using Hartree potential. The energy eigenvalue and wave functions of exciton and the biexciton are obtained using the self-consistent technique. The effective mass approximation and BenDaniel-Duke boundary conditions are used in the self-consistent calculations. The pressure-induced nonlinear optical absorption coefficients for the heavy hole exciton and the biexciton as a function of incident photon energy for CdTe/ZnTe quantum dot are investigated. The optical gain coefficient with the injection current density, in the presence of various hydrostatic pressure values, is studied in a CdTe/ZnTe spherical quantum dot. The pressure-induced threshold optical pump intensity with the dot radius is investigated. The results show that the pressure-induced electronic and optical properties strongly depend on the spatial confinement effect.     

The Polaron Self-Energy in a Parabolic Quantum Dot

Polaronic states in a parabolic quantum dot are investigated by using the second order Rayleigh-Schrödinger perturbation theory. It is shown that the absolute values of the ground state energy correction and the excited state energy correction as well as the relevant transition energies increase with decreasing the size of the quant um dot. The results also indicate that the polaron effects in small quantum dots are stronger than those in the corresponding bulk materials.     

Optical properties of an off-center hydrogenic impurity in a spherical quantum dot with Gaussian potential

Optical absorption coefficients and refractive index changes associated with intersubband transition of an off-center hydrogenic impurity in a spherical quantum dot (QD) with Gaussian confinement potential are theoretically investigated. Our results show that the optical absorption coefficients in a spherical QD are 2–3 orders of magnitude higher than those in quantum wells and are 2–3 orders smaller than those in a disk-like QD. It is found that the optical absorptions and the optical refractive index are strongly affected not only by the confinement barrier height, dot radius but also by the position of the impurity.     

Effects of hydrostatic pressure on the donor impurity in a cylindrical quantum dot with Morse confining potential

The effects of hydrostatic pressure and size quantization on the binding energies of a hydrogen-like donor impurity in cylindrical GaAs quantum dot (QD) with Morse confining potential are studied using the variational method and effective-mass approximation. In the cylindrical QD, the effect of hydrostatic pressure on the binding energy of electron has been investigated and it has been found that the application of the hydrostatic pressure leads to the blue shift. The dependence of the absorption edge on geometrical parameters of cylindrical QD is obtained. Selection rules are revealed for transitions between levels with different quantum numbers. It is shown that for the radial quantum number, transitions are allowed between the levels with the same quantum numbers, and any transitions between different levels are allowed for the principal quantum number.     

Effects of electric field and size on the electron-phonon interaction in a spherical quantum dot with impurity

The effects of electric field and size on the electron-phonon interaction with an on-center impurity in a Zn_1?x Cd _x Se/ZnSe spherical quantum dot are studied, taking into account the interactions with confined, half-space and surface optical phonons. In addition, the interaction between impurity and phonons has also been considered. The results show that the electron-confined, electron-half-space, and electron-surface optical phonon interaction energies are all negative. The electron-confined optical phonon interaction energy is weakened by the electric field, but the electron-half-space and electron-surface optical phonon interaction energies are strengthened by it. In particular, the electron-surface optical phonon interaction depends strongly on the electric field, and it will vanish when the electric field is absent. It is also found that the electron-confined optical phonon interaction and electron-impurity “exchange” interaction energies reach a peak values as the quantum dot radius increases and then gradually decrease, but the electron-half-space optical phonon interaction energy exponentially quickly approaches 0 as the quantum dot radius increases.     

Effect of conduction band parabolicity on the spectrum and binding energy of a hydrogenic impurity in GaAs spherical quantum dots

The energy levels and binding energies of a hydrogenic impurity in GaAs spherical quantum dots with radius R are calculated by the finite difference method. The system is assumed to have an infinite confining potential well with radius R, which can be viewed as a hard wall boundary condition. The parabolicity of the conduction band profile for GaAs material can be viewed as a parabolic potential well. The energy levels and binding energies are depended dramatically on the radius of the quantum dot and the parabolic potential well. The results show that parabolic potential can remarkably alter the energy level ordering and binding energy level ordering of hydrogenic impurity states for the quantum dot with a smaller radius R.     

Donor binding energies and spin-orbit coupling in a spherical quantum dot

The ground state and a few excited state energies of a hydrogenic donor in a spherical quantum dot (GaAs in a GaAlAs matrix) are computed. While the 1s and the 2s-state energies behave normally for dots of all radii, the 2p₀ and 2p_± states are unbound for most of the radii of interest. It is predicted that a semiconductor quantum dot with a hydrogenic donor will exhibit photoconductivity for a low threshold wavelength ∼12 μm. The spin-orbit coupling gives a contribution of the order of 10⁻⁵ meV for both 2p₀ and 2p_± states.