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Approximate methods for the solution of quantum wires and dots : Connection rules between pyramidal, cuboidal, and cubic dots

Califano, M. and Harrison, P. (1999) Approximate methods for the solution of quantum wires and dots : Connection rules between pyramidal, cuboidal, and cubic dots. Journal of Applied Physics, 86 (9). pp. 5054-5059. ISSN 1089-7550

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Energy eigenvalues of the electronic ground state are calculated for rectangular and triangular GaAs/Ga(0.6)Al(0.4)As quantum wires as well as for cuboidal and pyramidal quantum dots of the same material. The wire (dot) geometries are approximated by a superposition of perpendicular independent finite one-dimensional potential wells. A perturbation is added to the system to improve the approximation. Excellent agreement with more complex treatments is obtained. The method is applied to investigate the ground state energy dependence on volume and aspect ratio for finite barrier cubic, cuboidal, and pyramidal quantum dots. It is shown that the energy eigenvalues of cubes are equal to those of cuboids of the same volume and aspect ratio similar to one. In addition, a relationship has been found between the volumes of pyramidal quantum dots (often the result of self-assembling in strain layered epitaxy) and cuboidal dots with the same ground state energy and aspect ratios close to one. © 1999 American Institute of Physics.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 1999 American Institute of Physics. Reproduced in accordance with the publisher's self-archiving policy. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Electronic & Electrical Engineering (Leeds) > Institute of Microwaves and Photonics (Leeds)
Depositing User: Repository Officer
Date Deposited: 01 Nov 2006
Last Modified: 05 Jun 2014 11:37
Published Version: http://dx.doi.org/10.1063/1.371478
Status: Published
Publisher: American Institute of Physics
Refereed: Yes
Identification Number: 10.1063/1.371478
URI: http://eprints.whiterose.ac.uk/id/eprint/1681

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