POSITION DEPENDENT EFFECTIVE MASSES FOR DONOR BINDING ENERGIES IN QUANTUM CONFINED SYSTEMS IN AN ELECTRIC FIELD

2010 ◽  
Vol 09 (01n02) ◽  
pp. 83-91 ◽  
Author(s):  
S. RAJASHABALA ◽  
KANNAN RAMAN
Keyword(s):  
Electric Field ◽  
Effective Mass ◽  
Binding Energies ◽  
Bohr Radius ◽  
Ionization Energies ◽  
Effective Masses ◽  
Hydrogenic Donor ◽  
Finite Barrier ◽  
Dependent Mass ◽  
Position Dependent Mass

In our earlier works, the effective mass theory (EMT) was critically examined for a hydrogenic donor in a quantum well (QW) and in a quantum dot (QD) after introducing position dependent effective masses (PDEMs). Our results showed that the use of constant effective mass was justified for all well dimensions a*, the effective Bohr radius which is 100 Å in GaAs. Here the validity of EMT in the presence of an electric field is examined. The electric field dependent donor ionization energies in both the systems with finite and infinite barriers for different well dimensions have been calculated. It is shown that the electric field affects donor binding energies appreciably, the variation being larger in the case of finite barrier systems when PDEM is used. The donor polarizability has also been estimated in both the systems and the results are compared with other works in the literature. The use of EMT is justified if constant effective mass is used in general, even though large variation in the ionization energies occur in the finite barrier cases when position dependent mass is included correctly.

EFFECTIVE MASSES FOR DONOR BINDING ENERGIES IN QUANTUM WELL SYSTEMS

2006 ◽  
Vol 20 (24) ◽  
pp. 1529-1541 ◽  
Author(s):  
S. RAJASHABALA ◽  
K. NAVANEETHAKRISHNAN
Keyword(s):  
Quantum Well ◽  
Effective Mass ◽  
Binding Energies ◽  
Bohr Radius ◽  
Mass Variation ◽  
Effective Masses ◽  
Approximate Form ◽  
Finite Barrier ◽  
Infinite Barrier ◽  
Barrier Model

The donor ionization energies in a quantum well and quantum dot with finite and infinite barriers are estimated for different well dimensions. Using the effective mass (EM) approximation, calculations are presented with constant effective mass and position dependent effective masses that are different for finite and infinite cases. Our results reduce to an approximate form used by X. H. Qi et al., Phys. Rev. B58 (1998) 10578 in the finite barrier model and that of L. E. Oliveira and L. M. Falicov, Phys. Rev. B34 (1986) 8676 in the infinite barrier case. Results are presented by taking the GaAs quantum well as an example. The use of constant effective mass of 0.067m0 is justified for well dimensions ≥a* where a* is an effective Bohr radius which is about 100 Å. While Qi et al. found a maximum of 22% variation in the binding energies due to mass variation, we obtained nearly 100% variation when mass variations are included correctly.

scholarly journals AUXILIARY QUANTIZATION CONSTRAINTS ON THE VON ROOS ORDERING-AMBIGUITY AT ZERO BINDING ENERGIES; AZIMUTHALLY SYMMETRIZED CYLINDRICAL COORDINATES

2013 ◽  
Vol 28 (19) ◽  
pp. 1350082
Author(s):  
OMAR MUSTAFA
Keyword(s):  
Binding Energies ◽  
Degree Of Freedom ◽  
Zero Energy ◽  
Cylindrical Coordinates ◽  
Additional Degree ◽  
Quantum Numbers ◽  
Dependent Mass ◽  
Position Dependent Mass

Using azimuthally symmetrized cylindrical coordinates, we report the consequences of zero-energy quantal states on the von Roos Hamiltonian. A position-dependent mass (PDM) M(ρ, φ, z) = bzjρ2υ+1/2 is used. We show that the zero-energy setting not only offers an additional degree of freedom toward feasible separability for the von Roos Hamiltonian, but also manifestly yields auxiliary quantized ambiguity parametric constraints (i.e. the ambiguity parameters are given in terms of quantum numbers).

EFFECT OF HYDROSTATIC PRESSURE ON THE BINDING ENERGIES OF EXCITONS IN QUANTUM WELLS

2007 ◽  
Vol 21 (16) ◽  
pp. 2735-2747 ◽  
Author(s):  
G. J. ZHAO ◽  
X. X. LIANG ◽  
S. L. BAN
Keyword(s):  
Dielectric Constant ◽  
Hydrostatic Pressure ◽  
Quantum Wells ◽  
Pressure Effect ◽  
Binding Energies ◽  
Band Offset ◽  
Conduction Band Offset ◽  
Effective Masses ◽  
Finite Barrier ◽  
Effect Of Hydrostatic Pressure

The binding energies of excitons in finite barrier quantum wells under hydrostatic pressure are calculated by a variational method. The influences of hydrostatic pressure on the effective masses of the electron and hole, the dielectric constant, and the conduction band offset between the well and barriers are taken into account in the calculation. The numerical results for the GaAs/Al x Ga 1-x As and GaN/Al x Ga 1-x N quantum wells are given respectively. It is shown that the exciton binding energy increases linearly with the pressure and the pressure effect on arsenide quantum wells is more obvious than that on nitride ones. The exciton binding energies monotonically increase with increasing barrier height, which is related to the Al concentration of the barriers and the influence of the pressure.

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

Open Physics ◽  
2005 ◽  
Vol 3 (4) ◽  
Author(s):  
Axel Schulze-Halberg
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Transport Phenomena ◽  
Quantum Systems ◽  
Time Dependent ◽  
Effective Masses ◽  
Dependent Mass ◽  
Position Dependent Mass

AbstractWe study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.

ELECTRIC FIELD EFFECTS ON POLARONS WITH SPATIALLY DEPENDENT MASS IN PARABOLIC QUANTUM WELLS

2004 ◽  
Vol 18 (22) ◽  
pp. 2991-2999 ◽  
Author(s):  
FENG-QI ZHAO ◽  
ZI-ZHENG GUO
Keyword(s):  
Electric Field ◽  
Quantum Wells ◽  
Effective Mass ◽  
Energy Levels ◽  
Longitudinal Optical ◽  
Optical Phonons ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Dependent Mass ◽  
Parabolic Quantum Wells

The free polaron energy levels in finite GaAs / Al x Ga 1-x As parabolic quantum wells have been investigated by a modified variational method. The effect of the electric field, the electron-phonon interaction including the longitudinal optical phonons and the four branches of interface optical phonons, and the effect of spatial dependent effective mass have been considered in the calculation. The dependence of the energies of free polarons on the alloy composition x is given. The numerical results for finite GaAs / Al x Ga 1-x As parabolic quantum wells are obtained and discussed. The results show that the effect of the electric field and the interface optical phonons as well as the longitudinal optical phonons on the energy levels is obvious. One can find that the effect of the spatially dependent effective masses on the energy levels in finite parabolic quantum wells is considerable except for large well width. Thus, the electron-phonon interaction and the effect of the spatially dependent effective mass should not be neglected for the study of the electron state problem in finite parabolic quantum wells.

INFLUENCE OF ELECTRIC FIELD ON THE BINDING ENERGY OF HYDROGENIC IMPURITY WITH SPATIALLY DEPENDENT MASS IN NITRIDE PARABOLIC QUANTUM WELLS

2007 ◽  
Vol 21 (05) ◽  
pp. 279-286 ◽  
Author(s):  
FENG-QI ZHAO ◽  
JIAN GONG
Keyword(s):  
Binding Energy ◽  
Electric Field ◽  
Quantum Wells ◽  
Ground State ◽  
Quantum Confinement Effect ◽  
Energy Levels ◽  
Binding Energies ◽  
Hydrogenic Impurity ◽  
Dependent Mass ◽  
Parabolic Quantum Wells

The ground state and binding energies of the hydrogenic impurity in a finite GaN/Al x Ga 1-x N parabolic quantum well (PQW) are investigated by using variational method. The effect of an electric field and spatial dependence effective mass (SDEM) are considered in the calculation. The results indicate that the effect of the SDEM on the energy levels is more obvious in the case of the narrower well width L. The effects decrease with increasing L, and tend to zero. The electric field shifts the energy levels towards lower energies with increasing well width L. Furthermore the ground state binding energy of the hydrogenic impurity in GaN/Al x Ga 1-x N PQWs is larger than that in GaAs/Al x Ga 1-x As PQWs. Therefore, we affirm that there is stronger quantum confinement effect in GaN/Al x Ga 1-x N PQW.

ALGEBRAIC APPROACH TO THE POSITION-DEPENDENT MASS SCHRÖDINGER EQUATION FOR A SINGULAR OSCILLATOR

2007 ◽  
Vol 22 (14) ◽  
pp. 1039-1045 ◽  
Author(s):  
SHI-HAI DONG ◽  
J. J. PEÑA ◽  
C. PACHECO-GARCÍA ◽  
J. GARCÍA-RAVELO
Keyword(s):  
Schrödinger Equation ◽  
Quantum System ◽  
Effective Mass ◽  
Lie Algebra ◽  
Schrodinger Equation ◽  
Algebraic Approach ◽  
Hidden Symmetry ◽  
Dependent Mass ◽  
Complete Solutions ◽  
Position Dependent Mass

We construct a singular oscillator Hamiltonian with a position-dependent effective mass. We find that an su(1, 1) algebra is the hidden symmetry of this quantum system and the isospectral potentials V(x) depend on the different choices of the m(x). The complete solutions are also presented by using this Lie algebra.

The synergistic effect between effective mass and built-in electric field for the transfer of carriers in nonlinear optical materials

2015 ◽  
Vol 17 (27) ◽  
pp. 17710-17717 ◽  
Author(s):  
Mengmeng Li ◽  
Ying Dai ◽  
Xiangchao Ma ◽  
Zhujie Li ◽  
Baibiao Huang
Keyword(s):  
Synergistic Effect ◽  
Electric Field ◽  
Effective Mass ◽  
Optical Materials ◽  
Nonlinear Optical ◽  
Nonlinear Optical Materials ◽  
Effective Masses

The transfer of carriers is promoted by the synergistic effect between effective masses and built-in electric field in K3B6O10X (X = Br, Cl).

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