Radiative life time of an exciton confined in a strained GaN/Ga1-xAlxN cylindrical dot: built-in electric field effects

The binding energy of an exciton in a wurtzite GaN/GaAlN strained cylindrical quantum dot is investigated theoretically.The strong built-in electric field due to the spontaneous and piezoelectric polarizations of a GaN/GaAlN quantum dot is included.Numerical calculations are performed using a variational procedure within the single band effective mass approximation.Valence-band anisotropy is included in our theoretical model by using different hole masses in different spatial directions.The exciton oscillator strength and the exciton lifetime for radiative recombination each as a function of dot radius have been computed.The result elucidates that the strong built-in electric field influences the oscillator strength and the recombination life time of the exciton.It is observed that the ground state exciton binding energy and the interband emission energy increase when the cylindrical quantum dot height or radius is decreased,and that the exciton binding energy,the oscillator strength and the radiative lifetime each as a function of structural parameters (height and radius) sensitively depend on the strong built-in electric field.The obtained results are useful for the design of some opto-photoelectronic devices.     

纤锌矿GaN柱形量子点中类氢施主杂质态

在有效质量近似和变分原理的基础上,选取含两个变分参数的波函数,研究了纤锌矿结构的GaN/AlxGa1-xN单量子点中类氢施主杂质体系的结合能随量子点(QD)尺寸以及杂质在量子点中位置的变化,并与以前使用不同尝试波函数的计算结果进行了比较。结果表明:由我们选取的两变分参数波函数得到的结果与前人选取的两变分参数波函数得到的结果相比有所改进,而与选取一个变分参数波函数得到的结果一致。同时我们还计算了体系的维里定理值随量子点半径的变化情况,所得结果与前人工作结果一致,说明本文选取的两变分参数波函数能很好地描述柱形量子点中施主杂质态的运动。     

Electric-field control of electron–hole wave functions in a wide quantum well

The electric field dependence of the electron/hole wave function and the radiation energy of an exciton in a Be-δ-doped 80 nm quantum well (QW) is studied experimentally and compared it with variational calculation. The photoluminescence (PL) spectra show Stark shifts depending on the gate electric field and PL intensity of the exciton of the first excited state has a dip in the electric-field dependence which reflects the node of the electron wave function.     

Donor electron in a quantum well under the influence of an electric field

The ionization energies and the polarizabilities of a donor in an isolated well of a quasi two dimensional (Q2D) GaAs/Ga_1−x Al _x As heterostructure have been obtained for different well widths including electron-lattice coupling. A wave function that properly reduces to the hydrogenic function in the limiting case has been used. For fields of the order of 10⁵ V/m, the ionization energies decrease slightly with electric fields for all well widths (10 nm to 50 nm) studied. Also for a given electric field, as the well width increases, the ionization energy decreases. For fields of the order of 10⁷ V/m and for smaller well widths (<10 nm), the ionization energy generally increases with electric field. The results also show that for electric fields of this order, no donor bound state associated with the lowest subband is possible for well widths greater than 20 nm. The polarizabilities estimated using the expression for the dipole operator show that as the well width increases, the polarizability values also increase and do not show any abnormal behaviour.     

Electric field effect on the binding energy of a hydrogenic impurity in coaxial GaAs/Al xGa1 − x As quantum well-wires

The ground state binding energy of a hydrogenic impurity in a coaxial cylindirical quantum well wire system subjected to an external electric field applied perpendicular to the symmetry axis of the wire system is studied within a variational scheme. Binding energy calculations were performed as functions of the inner barrier thickness and the electric field for two different impurity positions. The main result is that a sharp decrease in the binding energy, which may be important in device applications, occurs in certain conditions.     

Phonon effect on binding energies of impurity states in cylindrical quantum wires of polar semiconductors under an electric field

Phonon effect on hydrogenic impurity states in cylindrical quantum wires of polar semiconductors under an applied electric field is studied theoretically by a variational approach. The binding energies are calculated as functions of the transverse dimension of the quantum wire, and the donor-impurity position under different fields. The electron–phonon interaction is considered in the calculations by taking both the confined bulk longitudinal optical phonons and interface optical phonons as well as the impurity-ion–phonon coupling. The numerical results for the CdTe and GaAs quantum wires are given and discussed as examples. It is confirmed that the electron–phonon interaction obviously reduces both the binding energy and the Stark energy-shift of the bound polarons in quantum wires.     

外电场对InGaAsP/InP量子阱内激子结合能的影响

在有效质量近似下采用变分法计算了InGaAsP/InP量子阱内不同In组分下的激子结合能,分析了结合能随阱宽和In组分的变化情况,并且讨论了外加电场对激子结合能的影响. 结果表明：激子结合能是阱宽的一个非单调函数,随阱宽的变化呈现先增加后减小的趋势;随着In组分增大,激子结合能达到最大值的阱宽相应变小,这与材料的带隙改变有关;在一定范围内电场的存在对激子结合能的影响很小,但电场强度较大时会破坏激子效应. 关键词： 激子 InGaAsP/InP量子阱 结合能 电场     

Comparison of external electric and magnetic fields effect on binding energy of hydrogenic donor impurity in different shaped quantum wells

The effects of external electric and magnetic fields on the ground state binding energy of hydrogenic donor impurity are compared in square, V-shaped, and parabolic quantum wells. With the effective-mass envelope-function approximation theory, the ground state binding energies of hydrogenic donor impurity in InGaAsP/InP QWs are calculated through the plane wave basis method. The results indicate that as the quantum well width increases, the binding energy changes most fast in SQW. When the well width is fixed, the binding energy is the largest in VQW for the donor impurity located near the center of QWs. For the smaller and larger well width, the electric field effect on binding energy is the most significant in VQW and SQW, respectively. The magnetic field effect on binding energy is the most significant in VQW. The combined effects of electric and magnetic fields on the binding energy of hydrogenic donor impurity are qualitative consistent in different shaped QWs.     

Photoionization of a charged exciton in a GaAs/GaAlAs corrugated quantum well

Binding energies of a charged exciton as a function of well width of a GaAs/GaAlAs corrugated quantum well are investigated. The calculations have been performed by the variational method based on a two parametric trial wave function within a single band effective mass approximation. We have also included the effect of nonparabolicity of the conduction band of GaAs. We study the spectral dependence of the charged exciton in a GaAs/GaAlAs corrugated quantum well as a function of well width. The photoionization cross section for the charged exciton placed at the center of the quantum well is computed as a function of normalized photon energy. The cross-section behavior as a function of incident energy is entirely different in the two cases of radiation being x-direction (along the growth direction) or z-direction. The interband emission energy as a function of well width is calculated and the dependence of the photoionization cross section on photon energy is carried out for the charged excitons. The resulting spectra are brought out for light polarized along and perpendicular to the growth direction. The results show that the charged exciton binding energy, interband emission energy and the photoionization cross section depend strongly on the well width. Our results are compared with the other existing literature available.     

The symmetry of the relative motion of excitons in semiconductor heterostructures

A theoretical model of excitonic states in semiconductor heterostructures is presented. The approach employs the envelope function approximation, and involves a two parameter variational calculation in which the symmetry of the component of the wave function representing the relative motion is allowed to vary between the two- and three-dimensional limits. Detailed calculations are described for a variety of single quantum wells and superlattices. The results show that the excitons are neither 2D nor 3D like, but are intermediate in character. Furthermore, in the main, they assume the symmetry of a prolate spheroid. An exception to this occurs in the special case of an asymmetric double quantum well close to resonance, where two stable exciton states are found for the same one-particle states. One of these ‘twin’ exciton states is an oblate spheroid. The results illustrate the need for accurate determination of excitonic properties if the dynamical evaluation of exciton states, in for example, quantum well lasers, is to be readily determined.     

Electric field induced nonlinear optical properties of a confined exciton in a ZnO/Zn1−xMgxO strained quantum dot

Electric field induced exciton binding energy as a function of dot radius in a ZnO/Zn_1−xMg_xO quantum dot is investigated. The interband emission as a function of dot radius is obtained in the presence of electric field strength. The Stark effect on the exciton as a function of the dot radius is discussed. The effects of strain, including the hydrostatic and the biaxial strain and the internal electric field, induced by spontaneous and piezoelectric polarization are taken into consideration in all the calculations. Numerical calculations are performed using variational procedure within the single band effective mass approximation. Some nonlinear optical properties are investigated for various electric field strengths in a ZnO/Zn_1−xMg_xO quantum dot taking into account the strain-induced piezoelectric effects. Our results show that the nonlinear optical properties strongly depend on the effects of electric field strength and the geometrical confinement.     

Electric field effects on the states of an exciton in square cross-section quantum well wires

The Letter studies the role of the external electric field on the binding energy of the exciton states in square cross-section quantum well wires. Using the effective-mass approximation within a variational scheme and expanding the wave function into Fourier series, we calculate the binding energies of the ground state as well as that of the excited states as the functions of the geometry and the strength of the applied electric field. In the presence of an electric field, it is found that for the ground state the Stark effect is redshift, and for the first and the second excited state the binding energy are split into two levels which will change in contrary situation along with the increasing of the strength of the applied electric field.     

Laser field induced interband absorption in a strained GaAs/GaAlAs double quantum well system

Effect of laser field intensity on exciton binding energies is investigated in a GaAs/ GaAlAs double quantum well system. Calculations have been carried out with the variational technique within the single band effective mass approximations using a two parametric trial wave function. The interband emission energy as a function of well width is calculated in the influence of laser field. The laser field induced photoionization cross-section for the exciton placed at the centre of the quantum well is computed as a function of normalized photon energy. The dependence of the photoionization cross-section on photon energy is carried out for the excitons. The resulting spectra are brought out for light polarized along and perpendicular to the growth direction. The intense laser field dependence of interband absorption coefficient is investigated. The results show that the exciton binding energy, interband emission energy, the photoionization cross-section and the interband absorption coefficient depend strongly on the well width and the laser field intensity. Our results are compared with the other existing literature available.     

Stark shift and dissociation process of an ionized donor bound exciton in spherical quantum dots

The effect of an electric field on the ground state energy of an exciton bound to an ionized donor (D⁺, X) was studied in CdSe spherical quantum dots where quantum confinement is described by an infinitly deep potential. Calculations have been performed in the framework of the effective mass approximation using a variational method by choosing an appropriate sixty-terms wave function taking into account different interparticles correlations and symetry distorsion induced by the electric field. It appears that the Stark shift is significant even for low fields and depends strongly of spherical dot sizes. The competition between the confinement effect and the Stark effect is discussed as function of the spherical dot size and the applied electric field strength. The (D⁺, X) Stark shift is estimated and its behavior is discussed as a function of the dot radius and electric field strength. The electron and hole average distances have also been calculated and the role of the ionized donor in the excitonic dissociation is established.     

Hydrostatic pressure and electric and magnetic field effects on the binding energy of a hydrogenic donor impurity in InAs Pöschl-Teller quantum ring

We consider the effects of electric and magnetic fields as well as of hydrostatic pressure on the donor binding energy in InAs Pöschl-Teller quantum rings. The ground state energy and the electron wave function are calculated within the effective mass and parabolic band approximations, using the variational method. The binding energy dependencies on the electric field strength and the hydrostatic pressure are reported for different values of quantum ring size and shape, the parameters of the Pöschl-Teller confining potential, and the magnetic field induction. The results show that the binding energy is an increasing or decreasing function of the electric field, depending on the chosen parameters of the confining potential. Also, we have observed that the binding energy is an increasing/decreasing function of hydrostatic pressure/magnetic field induction. Likewise, the impurity binding energy behaves as an increasing/decreasing function of the inner/outer radii of the quantum ring nanostructure.     

Magnetic field induced diamagnetic susceptibility of a hydrogenic donor in a GaN/AlGaN quantum dot

The binding energies of a hydrogenic donor in a GaN/AlGaN quantum dot are calculated in the influence of magnetic field. The calculations are carried out using the single-band effective mass approximation within a variational scheme. The magnetic field induced binding energy and diamagnetic susceptibility of the hydrogenic donor are obtained as a function of dot radius. Calculations have been carried out with and without the Zeeman effect through the energy-dependent effective mass. The diamagnetic shift of the hydrogenic donor is found for different dot radii. Our results show that (i) the binding energy is higher for smaller dot radii and the magnetic field effects are predominant for larger dot sizes, (ii) the binding energy is higher when the Zeeman effect is included for all the magnetic fields, (iii) the diamagnetic susceptibility increases with the magnetic field and is not pronounced for smaller dot radii and (iv) the diamagnetic shift has a good influence of larger dot radii.     

Polaron effects on the binding energy of a hydrogenic impurity in parabolic quantum wires in perpendicular electric and magnetic fields

Using a variational approach, the binding energy of shallow hydrogenic impurities in a parabolic quantum wire is calculated within the effective mass approximation. The polaron effects on the ground-state binding energy in electric and magnetic fields are investigated by means of the Pekar–Landau variation technique. The results for the binding energy as well as a polaronic correction are obtained as a function of the applied fields and the impurity positions.     

Electronic states of a hydrogenic impurity in a zinc-blende GaN/AlGaN quantum well

Binding energies of ground and a few low lying excited states of a hydrogenic donor confined in a zinc-blende GaN/AlGaN quantum well are investigated. They are computed within the framework of single band effective mass approximation, by means of a variational approach. The donor states are investigated with the various impurity positions as a function of well width. The calculations have been carried out with the inclusion of conduction band non-parabolicity through the energy dependent effective mass. The variational solutions have been improved by using a two-parametric trial wavefunction. The results seem better and good agreement with the other investigators. To support our results, we observe that the values of variational parameters are consistent when two parameter wave function is used. We find that the inclusion of non-parabolic effects leads to more binding for all the values of well width and is significant for narrow wells. The results are compared with the existing available literature.     

Electric and magnetic field effects on the binding energy of a hydrogenic impurity in quantum well wires with different shapes

In this work, we directly calculate the ground state energies for an electron in quantum well wires (QWWs) with different shapes in the presence of applied electric and magnetic fields using the finite difference method. Then, we study the ground state binding energy of a hydrogenic impurity with a variational approach. We obtain the binding energy for QWWs consisting of the combinations of square and parabolic well potential. Our results indicate that the impurity binding energy depends strongly on the structural confinement and also, on the applied electric and magnetic field.     

Polaronic exciton in quantum wells wires and nanotubes

We investigate the effect of the longitudinal-optical phonon field on the binding energies of excitons in quantum wells, well-wires and nanotubes based on ionic semiconductors. We take into account the exciton-phonon interaction by using the Aldrich-Bajaj effective potential for Wannier excitons in a polarizable medium. We extend the fractional-dimensional method developed previously for neutral and negatively charged donors to calculate the exciton binding energies in these heterostructures. In this method, the exciton wave function is taken as a product of the ground state functions of the electron polaron and hole polaron with a correlation function that depends only on the electron-hole separation. Starting from the variational principle we derive a one-dimensional differential equation, which is solved numerically by using the trigonometric sweep method. We find that the potential that takes into account polaronic effects always give rise to larger exciton binding energies than those obtained using a Coulomb potential screened by a static dielectric constant. This enhancement of the binding energy is more considerable in quantum wires and nanotubes than in quantum wells. Our results for quantum wells are in a good agreement with previous variational calculations. Also, we present novel curves of the exciton binding energies as a function of the wire and nanotubes radii for different models of the confinement potential.