Quantum-well Wires Research Articles

Laser effects on donor states in low-dimensional semiconductor heterostructures

A theoretical study of the effects of intense laser fields on the ground-state binding energies of donor impurities in low-dimensional semiconductor heterostructures is performed. The laser-heterostructure interaction is treated within an extended dressed-atom approach, so that, for a laser tuned far below any resonances, the effects of the laser-semiconductor interaction correspond to a renormalization of the semiconductor energy gap and conduction/valence effective masses. Calculations are performed for donors in $\mathrm{GaAs}\text{\ensuremath{-}}(\mathrm{Ga},\mathrm{Al})\mathrm{As}$ quantum wells, cylindrical quantum-well wires, and spherical quantum dots. The binding energies of donors in low-dimensional systems increase with increasing laser intensity, and for a fixed intensity, the influence of the laser is stronger for small detunings. Results obtained within the extended dressed-atom approach are compared with previous calculations performed by using a simplified high-frequency limit of the Kramers-Henneberger approach.

Electric field effect on the binding energy of a non‐hydrogenic donor impurity in a cylindrical cross‐sectional quantum well wire

AbstractThe effect of an electric field on the non‐hydrogenic binding energy of a shallow donor impurity in a cylindrical cross‐sectional GaAs‐(Ga,Al)As quantum well wire (QWW) was investigated. Within the effective mass approximation, the non‐hydrogenic binding energy of the donor impurity was calculated by a variational method as a function of the wire radius, donor impurity position and applied electric field. The results show that the non‐hydrogenic binding energy of the donor impurity located around the centre is larger than that of the hydrogenic binding energy. The difference in binding energy of an on‐centre shallow donor impurity in the two regimes increases more rapidly with decreasing QWW radius than for other impurity positions. It has been found that the sensitivity of the donor binding energies to the applied electric field in both regimes is almost the same. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Polaron effects on third-harmonic generation in cylindrical quantum-well wires

Polaron effects on third-harmonic generation (THG) in cylindrical quantum wires with a finite confining potential are investigated. The THG coefficient is obtained by using the compact-density-matrix approach and an iterative method, and the numerical results are presented for GaAs/AlAs cylindrical quantum wires. The results show that the THG coefficient is greatly enhanced and the peak shift to the aspect of high energy when considering the influence of electron–phonon interaction.

Polar Oscillation of Interface and Surface Optical Phonons in Free-Standing Cylindrical Quantum-Well Wires**The project supported partly by Natural Science Foundation of Guangdong Province of China

Under dielectric continuum approximation, interface optical (IO) and surface optical (SO) phonon modes as well as the corresponding Fröhlich electron-phonon interaction Hamiltonian in a free-standing cylindrical quantum-well wire (QWW) are derived and studied. Numerical calculations on As cylindrical QWW are performed. Results reveal that there are two branches of IO phonon modes and one branch of SO phonon mode, and the dispersion frequencies of IO or SO phonon modes sensitively depend on the Al mole fraction in As material and the wave-vector in direction, . With the increasing of and quantum number , the frequency of each IO mode approaches one of the two frequency values of the single As heterostructure, and the electrostatic potential distribution of the phonon mode tends to be more and more localized at a certain interface or surface, meanwhile, the coupling between the electron-IO and -SO phonons becomes weaker.

One phonon resonant Raman scattering in quantum wires and free standing wires

We have developed a theory of one phonon resonant Raman scattering in a semiconductor quantum-well wire (QWW) and free standing wire (FSW) of cylindrical geometry. We present a complete description of the phonon modes of cylindrical structures embedded in another material, including a correct treatment of the mechanical and electrostatic matching conditions at the surface. We consider the Fröhlich interaction for resonance Raman scattering. Electron states are considered confined within the QWW and the FSW. We also assume T=0K and single parabolic conduction and valence bands. The spectra are discussed for different laser energies and the selection rules for the processes are also studied. Singularities in the spectra are found and interpreted.

Chemisorption on a quantum-well wire

The specific features of chemisorption on a quantum-well wire are studied. It is shown that the energy of an electron of an adatom chemisorbed on the quantum-well wire changes jumpwise with variations in the wire radius.

Variational Calculations of Neutral Bound Excitons in GaAsQuantum-Well Wires

The binding energy of an exciton bound to a neutral donor (D0,X)in GaAs quantum-well wires is calculated variationally as a function ofthe wire width for different positions of the impurity inside the wireby using a two-parameter wavefunction. There is no artificialparameter added in our calculation. The results we have obtained showthat the binding energies are closely correlated to the sizes of thewire, the impurity position, and also that their magnitudes are greaterthan those in the two-dimensional quantum wells compared. In addition,we also calculate the average interparticle distance as a function ofthe wire width. The results are discussed in detail.

Exciton and donor binding energies in quantum-well wires and quantum dots a fractional-dimensional space approach

A simple method for calculating the free-exciton binding energies in the fractional-dimensional-space model for single-quantum-well structure has been extended to quantum-well wires and quantum dots, in which the real anisotropic system is modelled through an effective isotropic environment with a fractional dimension. In this scheme, the fractional-dimensional parameter is chosen via an analytical procedure and involves no ansatz. We calculated the ground-state binding energies of excitons and donors in quantum-well wires with rectangular cross sections. Our results are found to be in good agreement with previous variational calculations and available experimental measurements. We also discussed the ground-state exciton binding energy changing with different shapes of quantum-well wires.

The electric field dependence of a donor impurity in graded GaAs quantum wires

The effect of the electric field on the binding energy of the ground state of a shallow donor impurity in a graded GaAs quantum-well wire (GQWW) was investigated. The electric field was applied parallel to the symmetry axes of the wire. Within the effective mass approximation, we calculated the binding energy of the donor impurity by a variational method as a function of the wire dimension, applied electric field, and donor impurity position. We show that changes in the donor binding energy in GQWWs strongly depend not only on the quantum confinement, but also on the direction of the electric field and on the impurity position. We also compared our results with those for the square quantum-well wire (SQWW). The results we obtained describe the behavior of impurities in both square and graded quantum wires.

The Einstein relation in nanostructured materials: simplified theory and suggestion for experimental determination

An attempt is made to study the Einstein relation for the diffusivity–mobility ratio (DMR) in quantum wells (QWs) and quantum well wires (QWWs) of tetragonal compounds on the basis of a newly formulated electron energy spectrum taking into account the combined influences of the anisotropies in effective electron mass, the spin–orbit splitting, and the presence of crystal field splitting, respectively. The results for quantum-confined III–V compounds form a special case of our generalized analysis. The DMR has also been studied for QWs and QWWs of II–VI and IV–VI materials. Taking QWs and QWWs of CdGeAs2, InAs, CdS and PbSe as examples, it was found that the DMR increases with increasing carrier statistics and decreasing film thickness respectively in various oscillatory manners emphasizing the influence of dimensional quantizations and the energy band constants in different cases. An experimental method of determining the DMR in nanostructures with arbitrary dispersion laws has also been suggested and the present simplified analysis is in agreement with the suggested relationship. The well-known results for nanostructures with parabolic energy bands have also been obtained as special cases from this generalized analysis under certain limiting conditions.

BARRIER THICKNESS DEPENDENCE OF OPTICAL ABSORPTION OF EXCITONS IN GaAs COUPLED QUANTUM WIRE

We have calculated the binding energy of excitons, and the interband optical absorption in rectangular coupled quantum-well wires of GaAs surrounded by Ga 1-x Al x As in effective-mass approximation, using the variational approach. Results obtained show that the exciton binding energies and optical absorption depend on the sizes of the wire and barrier thickness. To the best of our knowledge the exciton binding energy and interband optical absorption in the rectangular coupled quantum wires have not been clarified yet.

TRANSFER MATRIX METHOD FOR THE FRÖHLICH ELECTRON–INTERFACE OPTICAL PHONON INTERACTION IN MULTILAYER COAXIAL CYLINDRICAL QUANTUM-WELL WIRES

Under dielectric continuum approximation, by adopting the transfer matrix method, interface optical (IO) phonon modes and the Fröhlich electron–IO-phonon interaction Hamiltonian in a multilayer coaxial cylindrical quantum-well wire (QWW) were deduced and investigated. Numerical calculations on a four-layer GaAs / Al x Ga 1-x As QWW have been performed. Results reveal that there are six branches of IO phonon modes. When the wave vector in z-direction kz and the azimuthal quantum number m are small, the dispersion frequencies of IO modes sensitively depend on kz and m. When kz and m are relatively large, with the increasing of kz and m, the frequency for each mode converges the limit frequency value of IO mode in single heterostructure, and the electrostatic potential distribution of each mode tends to be more and more localized at the interfaces, meanwhile, the coupling between the electron–IO-phonon becomes weaker and weaker. The calculation also shows that the phonon modes with higher frequencies have more significant contribution to the electron–phonon interaction. At last, it is found that kz and m have analogous effects on the frequencies and the electrostatic potentials of the IO phonons.

Density of electronic states in impurity-doped quantum well wires

We analyze the electronic states in the cylindrical quantum well-wire (QWW) with randomly distributed neutral, D 0 and negatively charged D − donors. In order to calculate the ground state energies of the off-center donors D 0 and D − as a function of the distance from the axis of QWW we use the recently developed fractal dimension method in which the problems are reduced to a similar one for a hydrogen-like atom and a negative-hydrogen-like ion respectively, in an isotropic effective space with variable fractional dimension. The numerical trigonometric sweep method and the three-parameter Hylleraas trial function are used to solve these problems. We present a novel curves for the density of impurity states in a cylindrical QWWs with square-well, parabolic and soft-edge barrier potentials. Additionally we analyze the effect of the repulsive core on the density of the impurity states.

Binding Energies of Excitons in Square Quantum-Well Wires inthe Presence of a Magnetic Field

The binding energies of the ground state of excitons in theGaAs/Ga1−xAlxAs square quantum-well wire in thepresence of a magnetic field are investigated by using the variationalmethod. It is assumed that the magnetic field is applied parallel tothe axis of the wire. The calculations of the binding energy as afunction of the wire size have been performed for infinite and finiteconfinement potentials. The contribution of the magnetic field makesthe binding energy larger obviously, particularly for the wide wire,and the magnetic field is much more pronounced for the binding energy ina square quantum wire than that in a cylindrical quantum wire. Themismatch of effective masses between the well and the barrier is alsoconsidered in the calculation.

Fröhlich Electron-Interface Optical Phonon Interactions in n-Layer Low-dimensional Coupling Quantum Structures

Within the framework of the dielectric continuum (DC) approximation, by using the transfer matrix method, uniform descriptions for the interface optical (IO) phonon modes and the Frhlich electron-IO phonon interaction Hamiltonians in n-layer coupling low-dimensional quantum systems (including the coupling quantum well (CQW), coupling quantum-well wire (CQWW) and coupling quantum dot (CQD)) have been deduced and investigated. Numerical calculation on three-layer AlGaAs/GaAs systems reveals that, when the wave-vector or quantum number in the three types of quantum confined systems (CQW, CQWW and CQD) approach infinity, each frequency of the IO phonon approaches one of the frequencies in single planar heterostructure, and the math and physical reasons for this feature have been explained and specified. The limited behavior of IO phonon frequency when the wave-vector or quantum number in these systems approach zero have also been displayed and analyzed.

The Einstein relation in quantum wells and quantum well wires: simplified theory and asuggestion for experimental determination

An attempt is made to study the Einstein relation for the diffusivity–mobility ratio(DMR) in quantum wells (QWs) and quantum well wires (QWWs) of tetragonalcompounds on the basis of a newly formulated electron energy spectrum takinginto account the combined influences of the anisotropies in the effective electronmass, the spin–orbit splitting and the presence of crystal field splitting. Thecorresponding results for QWs and QWWs of III–V compounds form a special case ofour generalized analysis. The DMR has also been studied for QWs and QWWsof II–VI and IV–VI materials. It has been found, taking QWs and QWWs ofCdGeAs2, InAs, CdS and PbSe as examples, that the DMR increases with increasing carrierdegeneracy and decreasing film thickness in various oscillatory manners, emphasizing theinfluence of dimensional quantization and the energy band constants in different cases. Anexperimental method for determining the DMR in QWs and QWWs having arbitrarydispersion laws has also been suggested and the present simplified analysis is in agreementwith the suggested relationship. The well-known results for QWs and QWWsof relatively wide gap materials having parabolic energy bands have also beenobtained as special cases from this generalized analysis under certain limitingconditions.

Optical transitions in quantum well wires under intense laser radiation

The influence of a laser-field on the exciton binding energy and interband optical transitions in quantum-well wires is calculated by using a variational method and in the effective mass approximation. We conclude that in quantum-well wires the laser field amplitude provides an important effect on the electronic and optical properties and the changes in the binding being dependent on the shape of the confinement potential.

Exciton absorption in quantum-well wires under the electric field

The binding energy of excitons, and interband optical absorption in quantum-well wires of GaAs surrounded by Ga 1− x Al x As is calculated in effective-mass approximation, using a variational approach. Results obtained show that the exciton binding energies, and optical absorption depend on the sizes of the wire and strength of the electric field. The additional confinement of particles in quantum well wire offers greater variety of electric field dependence in comparison to bulk materials and quantum well structures.

Off-Center Neutral and Negatively Charged Donor Impurities in Semiconductor Heterostructures: Fractal Dimension Method

We reduce the problems of the on- and off-center D0 and D— S-states in semiconductor heterostructures to the similar ones in an isotropic effective space with variable fractional dimension starting from the variational principle. The dimension of this space is defined as a scaling parameter that relates the radii of a set of spherical boxes to the charge densities within induced by the free electron ground state in the heterostructure. Explicit expressions for the effective space dimensionality in a quantum well (QW), quantum-well wire (QWW) and a quantum dot (QD) are found by using this definition. To solve the wave equations for the free electron ground state in the heterostructure and for the hydrogen-like atom S-states in the fractional-dimensional space, we use the numerical trigonometric sweep method. The three-parameter Hylleraas trial function is used to solve the similar problem for a negative-hydrogen-like ion in the effective space. Ground state binding energies for off-center neutral and negatively charged donors in QWs and spherical QDs are calculated. Our results are in a good agreement with those of the variational and Monte Carlo methods. In addition, novel results for the D— binding energy as a function of the cylindrical GaAs/Ga0.7Al0.3As QWW radius and the magnetic field intensity are presented. It is found that the D— binding energy in the wire increases from 0.055 Ry* up to about 1.230 Ry* as the radius decreases to 30 Å. It is also shown that the magnetic field produces a considerable enhancement of negative-donor binding energy in QWW only for radii greater than 100 Å.

The effect of a strong magnetic field on the binding energy and the photoionization process in quantum-well wires

Within the effective-mass approximation, we have investigated the influence of a strong magnetic field on the ground state binding energy and the photon energy dependence of the photoionization cross-section of a shallow donor impurity in a quasi-one-dimensional rectangular quantum wire with infinite and finite potential barriers, using a variational approach. It is found that the binding energy and the photoionization cross-section as a function of photon energy were drastically dependent on the sizes of the wire, the potential well heights and the applied magnetic field.