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Number of results

Journal

2008 | 6 | 1 | 97-104

Article title

Exact analytical solutions for shallow impurity states in symmetrical paraboloidal and hemiparaboloidal quantum dots

Content

Title variants

Languages of publication

EN

Abstracts

EN
The problem of a shallow donor impurity located at the centre of a symmetrical paraboloidal quantum dot (SPQD) is solved exactly. The Schrödinger equation is separated in the paraboloidal coordinate system. Three different cases are discussed for the radial-like equations. For a bound donor, the energy is negative and the solutions are described by Whittaker functions. For a non-bound donor, the energy is positive and the solutions become coulomb wave functions. In the last case, the energy is equal to zero and the solutions reduce to Bessel functions. Using the boundary conditions at the dot surfaces, the variations of the donor kinetic and potential energies versus the size of the dot are obtained. The problem of a shallow donor impurity in a Hemiparaboloidal Quantum dot (HPQD) is also studied. It is shown that the wave functions of a HPQD are specific linear combinations of those of a SPQD.

Publisher

Journal

Year

Volume

6

Issue

1

Pages

97-104

Physical description

Dates

published
1 - 3 - 2008
online
26 - 3 - 2008

Contributors

author
  • Laboratoire d’Electronique et Optique des Nanostructures de Semiconducteurs, Faculté des Sciences, Département de Physique, B. P. 20, El Jadida, Morocco
  • Département de Mathématiques, Centre Pédagogique Régional, El Jadida, Morocco
author
  • Ecole Normale Supérieure d’Enseignement Technique, Mohammedia, Morocco
  • Institut de Physique et d’Electronique de Metz, 1 Boulevard Arago, 57078, Metz, France

References

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Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-008-0070-9
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