The Binding Energies of Shallow Donor Impurities in GaAs–(Ga,Al)As Coaxial Quantum-Well Wires

Mikhailov, I.D.; Escorcia, R.; Sierra-Ortega, J.

doi:10.1002/1521-3951(200007)220:1<195::aid-pssb195>3.3.co;2-8

phys. stat. sol. (b)

2000

DOI: 10.1002/1521-3951(200007)220:1<195::aid-pssb195>3.3.co;2-8

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The Binding Energies of Shallow Donor Impurities in GaAs–(Ga,Al)As Coaxial Quantum-Well Wires

I.D. Mikhailov¹,

R. Escorcia²,

J. Sierra-Ortega³

Abstract: Within the effective-mass approximation a simple method to calculate the spectra of a shallowdonor impurity in GaAs±(Ga, Al)As cylindrical quantum-well wires (QWWs) suitable for any confinement potential shape in radial direction is proposed. A trial function is taken as the product of a hydrogenic part with two envelope functions: the ground state wave function of the uncoupled electron in quantum-well wire f k (r), and a variational function j(z) that describes the orbit confinement in axial direction. A Sch… Show more

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“…In addition, other approaches have been used to analyze the similar problem for the neutral impurity donor and the exciton. One of them, the fractional dimension [15,16] or its modification fractal dimension [17] method, permits to find the binding energy with high accuracy avoiding tedious calculations, typical for other methods. However, in spite of its simplicity up to now this method has not been used to analyze D À spectra in heterostructures.…”

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Negative-Donor in Graded Quantum Well-Wire: Fractal Dimension Approach

Sierra‐Ortega

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Mikhailov

2002

phys. stat. sol. (b)

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Ground state energy of a D 0 and D À placed at the axis of a GaAs/(Ga,Al)As cylindrical quantumwell-wire (QWW) in the presence of an external magnetic field oriented along the growth axis is calculated within the framework of effective-mass approximation. A model of confinement with a soft-barrier profile produced by a gradual variation of the Al concentration in the transition region of the junctions is considered. The one-and two-particle problems in a homogeneous space with cylindrical symmetry are reduced to similar problems in an effective non-homogeneous isotropic space by using the fractal dimension method. The variable fractal dimension in this space is expressed in terms of the unbounded electron ground state wave function, which we find by using trigonometric sweep method. The D À binding energy as a function of the graded GaAs/ Ga 0.7 Al 0.3 As QWW radius for different values of the transition region thickness and the magnetic field intensity are calculated by using the Hylleraas procedure. It is found that the D À binding energy increases from 0.055 Ry * up to about 1.230 Ry * as the radius decreases from infinity up to 30 A. It is shown that the magnetic field and a smoothing confining potential produce a considerable enhancement of negative-donor binding energy, only for radii greater than 100 A.Introduction A neutral shallow donor impurity confined in quantum wells (QWs) can readily bind a second electron to form a negatively charged ion D À , stable in a strong magnetic field up to room temperature [1-3]. Initially found in bulk only under metastable conditions [4], a negative-donor is analogous to the H À ion, which offers an interesting example of a few-particle system where the electron-electron correlation plays a decisive role in trapping and keeping of a second electron [5,6]. The diffusion quantum Monte Carlo [7] and variational [8][9][10][11][12][13][14] methods have been used to calculate the D À ground state binding energy in semiconductor heterostructures. An increasing of the D À binding energy up to 10 times in QWs and up to 50 times in quantum dots (QDs) produced by the confinement has been found. In addition, other approaches have been used to analyze the similar problem for the neutral impurity donor and the exciton. One of them, the fractional dimension [15,16] or its modification fractal dimension [17] method, permits to find the binding energy with high accuracy avoiding tedious calculations, typical for other methods. However, in spite of its simplicity up to now this method has not been used to analyze D À spectra in heterostructures. On the other hand, there is very limited information [14,18] about the D À electronic spectra calculations in QWW and the effect of the magnetic field in this heterostructure has not been investigated.In this work we use the fractal dimension (FD) method to calculate the ground state binding energy of a neutral and a negatively charged donor centered in a graded cylind-

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confidence: 99%

Negative-Donor in Graded Quantum Well-Wire: Fractal Dimension Approach

Sierra‐Ortega

Betancur

Mikhailov

2002

phys. stat. sol. (b)

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The Binding Energies of Shallow Donor Impurities in GaAs–(Ga,Al)As Coaxial Quantum-Well Wires

Cited by 1 publication

References 8 publications

Negative-Donor in Graded Quantum Well-Wire: Fractal Dimension Approach

Negative-Donor in Graded Quantum Well-Wire: Fractal Dimension Approach

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