Effects of a Diffuse Potential on Shallow-Donor States in GaAs-(Ga,Al)As Quantum Dots

Betancur, Fernando Jaramillo; Mikhailov, I. D.; Sierra, Jhonatan Camilo Porto

doi:10.1002/(sici)1521-3951(199807)208:1<51::aid-pssb51>3.0.co;2-l

Cited by 6 publications

(4 citation statements)

References 14 publications

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“…The influence of dimensional quantization on a shallow hydrogenic impurity has been also studied (e.g. see [6,7]). The basic results have been derived by Bastard [2], where the binding energy of an impurity in a quantum well was calculated by the variational method.…”

Section: Introductionmentioning

confidence: 99%

Hydrogenic impurity in two-dimensional semiconductors with anisotropic energy spectrum of carriers

Andreev

Павлова

2005

Laser Phys. Lett.

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The binding energy and wave function of a ground state of a shallow hydrogenic impurity in two-dimensional semiconductors with isotropic and anisotropic effective mass of carriers m * = { m ⊥, m ⊥, m || } are derived. The calculations are performed by the variational method based on a two-parametric trial wave function. The dependence of binding energy and deformation of an impurity on 2D layer thickness and effective mass anisotropy parameter m ⊥ / m || is investigated. The obtained results are in a good agreement with experimental data and in the limiting cases coincide with the theoretical calculations of shallow impurity binding energy for bulk semiconductors [1] and two-dimensional semiconductors with isotropic effective mass of electrons [2].

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Section: Introductionmentioning

confidence: 99%

Hydrogenic impurity in two-dimensional semiconductors with anisotropic energy spectrum of carriers

Andreev

Павлова

2005

Laser Phys. Lett.

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“…To verify this assumption one can use the expression for the critical well wire radius R c =a * 0 % 3 Ry * =V 0 1=2 for which the electronic subband energies in QWW with barrier height V 0 are pushed out QW. According to this formula, which can be deduced by using the uncertainty relation similarly as it has been done for quantum dots in [9,11], the significant wave function leakage into the interior barrier regions occurs when the QWW radius decreases up to 0:2R c =a * 0 % 3=40 1=2 and hence R c a * 0 % 1:37. This is in a good agreement with the position of the smaller peak (R a * 0 % 1:30 ) for 1s-like state presented in Fig.…”

Section: Resultsmentioning

confidence: 99%

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

Mikhailov¹,

Escorcia²,

Sierra-Ortega³

2000

phys. stat. sol. (b)

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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 Schro È dinger-type equation for j(z) corresponding to the best trial function is deduced. The method is applied to analyze the D 0 ground and first excited states in coaxial cylindrical QWWs. Two peaks in the curve of the 1s-like state binding energy vs. the QWW radius are found.

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“…Recently, Bose [25] and Bose and Sarkar [24,26,27] studied the binding energy of impurity in the QD with a computational tedious variational method and showed that the simple perturbation method is able to yield fairly accurate results even in the regime of moderate confinement. Betancur and coworkers [28][29][30][31] have also calculated the energy states of oncentre donors in the QD with the variational method. All of the previous calculations showed that the binding energy of the impurity atom in a quantum well depends prominently on the barrier height V 0 and the well (dot) size.…”

Section: Introductionmentioning

confidence: 99%

Donor states in a multi-layered quantum dot

Hsieh¹,

Chuu

2000

J. Phys.: Condens. Matter

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The ground and excited state energies of a hydrogenic impurity located at the centre of a multi-layered quantum dot (MLQD) are calculated in the framework of the effective-mass approximation. The MLQD consists of a spherical core (e.g. GaAs) and a coated spherical shell (e.g. Ga 1−x Al x As). The whole dot is then embedded inside a bulk material (e.g. Ga 1−y Al y As). We solve the Schrödinger equation exactly. The eigenfunctions of the impurity are expressed in terms of Whittaker function and Coulomb wavefunction. The state energies are expressed in terms of the shell thickness, core radius, total dot radius and the potential heights. Our calculation shows that, as the dot radius approaches infinity, the state energies of an impurity located at the centre of a multi-layered or a single-layered QD approach −1/n 2 Ry, where n is the principal quantum number, Ry = µe 4 /2ε 2h2 , µ and ε are the electronic effective mass and the dielectric constant of GaAs material. Thus it behaves like a three-dimensional free hydrogen atom. For very small dot radius, however, the state energy of the hydrogenic impurity of a MLQD behaves very differently from that of a single-layered QD. For a multi-layered QD with finite shell and bulk potential barrier heights, the state energies of the impurity are found to be dependent on the difference of the shell potential (V 2) and the bulk potential (V 3).

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Effects of a Diffuse Potential on Shallow-Donor States in GaAs-(Ga,Al)As Quantum Dots

Cited by 6 publications

References 14 publications

Hydrogenic impurity in two-dimensional semiconductors with anisotropic energy spectrum of carriers

Hydrogenic impurity in two-dimensional semiconductors with anisotropic energy spectrum of carriers

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

Donor states in a multi-layered quantum dot

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