Energy spectra of an electron in a pyramid-shaped quantum dot in effective mass approximation with even mirror boundary conditions

Yuri Vorobiev; Vítor Vieira; Pedro Ribeiro; Valentina Gorley; Paul Horley; Jesús González-Hernández; Tetyana Torchynska

Energy spectra of an electron in a pyramid-shaped quantum dot in effective mass approximation with even mirror boundary conditions

Yuri Vorobiev, Vítor Vieira, Pedro Ribeiro, Valentina Gorley, Paul Horley, Jesús González-Hernández, Tetyana Torchynska

Escuela Superior de Física y Matemáticas (ESFM)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

We study the problem of an electron confined in a semiconductor quantum dot shaped as a squarebase pyramid, assuming specular reflection of a particle from quantum dot boundaries. The application of boundary condition equals the wave function in an arbitrary point inside the dot with its image formed in the walls, allowing to find wave the functions and energy spectra of the particle. The comparison of the resulting energies with published experimental data shows reasonable agreement between the theory and the experiment.

Translated title of the contribution	Espectros de energía de un electrón en un punto cuántico en forma de pirámide en aproximación de masa efectiva con condiciones de contorno de espejo uniforme
Original language	English
Title of host publication	10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11
Pages	127-131
Number of pages	5
State	Published - 2011
Event	10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11 - Cambridge, United Kingdom Duration: 20 Feb 2011 → 22 Feb 2011

Publication series

Name	10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology, Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int.Conf. on IPLAFUN'11

Conference

Conference	10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11
Country/Territory	United Kingdom
City	Cambridge
Period	20/02/11 → 22/02/11

Keywords

Mirror boundary conditions
Pyramid
Quantum dot
Schrödinger equation

Cite this

Vorobiev, Y., Vieira, V., Ribeiro, P., Gorley, V., Horley, P., González-Hernández, J., & Torchynska, T. (2011). Energy spectra of an electron in a pyramid-shaped quantum dot in effective mass approximation with even mirror boundary conditions. In 10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11 (pp. 127-131). (10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology, Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int.Conf. on IPLAFUN'11).

Vorobiev, Yuri ; Vieira, Vítor ; Ribeiro, Pedro et al. / Energy spectra of an electron in a pyramid-shaped quantum dot in effective mass approximation with even mirror boundary conditions. 10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11. 2011. pp. 127-131 (10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology, Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int.Conf. on IPLAFUN'11).

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abstract = "We study the problem of an electron confined in a semiconductor quantum dot shaped as a squarebase pyramid, assuming specular reflection of a particle from quantum dot boundaries. The application of boundary condition equals the wave function in an arbitrary point inside the dot with its image formed in the walls, allowing to find wave the functions and energy spectra of the particle. The comparison of the resulting energies with published experimental data shows reasonable agreement between the theory and the experiment.",

keywords = "Mirror boundary conditions, Pyramid, Quantum dot, Schr{\"o}dinger equation",

author = "Yuri Vorobiev and V{\'i}tor Vieira and Pedro Ribeiro and Valentina Gorley and Paul Horley and Jes{\'u}s Gonz{\'a}lez-Hern{\'a}ndez and Tetyana Torchynska",

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series = "10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology, Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int.Conf. on IPLAFUN'11",

pages = "127--131",

booktitle = "10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11",

note = "10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11 ; Conference date: 20-02-2011 Through 22-02-2011",

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Vorobiev, Y, Vieira, V, Ribeiro, P, Gorley, V, Horley, P, González-Hernández, J & Torchynska, T 2011, Energy spectra of an electron in a pyramid-shaped quantum dot in effective mass approximation with even mirror boundary conditions. in 10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11. 10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology, Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int.Conf. on IPLAFUN'11, pp. 127-131, 10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11, Cambridge, United Kingdom, 20/02/11.

Energy spectra of an electron in a pyramid-shaped quantum dot in effective mass approximation with even mirror boundary conditions. / Vorobiev, Yuri; Vieira, Vítor; Ribeiro, Pedro et al.
10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11. 2011. p. 127-131 (10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology, Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int.Conf. on IPLAFUN'11).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Energy spectra of an electron in a pyramid-shaped quantum dot in effective mass approximation with even mirror boundary conditions

AU - Vorobiev, Yuri

AU - Vieira, Vítor

AU - Ribeiro, Pedro

AU - Gorley, Valentina

AU - Horley, Paul

AU - González-Hernández, Jesús

AU - Torchynska, Tetyana

PY - 2011

Y1 - 2011

N2 - We study the problem of an electron confined in a semiconductor quantum dot shaped as a squarebase pyramid, assuming specular reflection of a particle from quantum dot boundaries. The application of boundary condition equals the wave function in an arbitrary point inside the dot with its image formed in the walls, allowing to find wave the functions and energy spectra of the particle. The comparison of the resulting energies with published experimental data shows reasonable agreement between the theory and the experiment.

AB - We study the problem of an electron confined in a semiconductor quantum dot shaped as a squarebase pyramid, assuming specular reflection of a particle from quantum dot boundaries. The application of boundary condition equals the wave function in an arbitrary point inside the dot with its image formed in the walls, allowing to find wave the functions and energy spectra of the particle. The comparison of the resulting energies with published experimental data shows reasonable agreement between the theory and the experiment.

KW - Mirror boundary conditions

KW - Pyramid

KW - Quantum dot

KW - Schrödinger equation

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M3 - Contribución a la conferencia

AN - SCOPUS:79958721705

SN - 9789604742769

T3 - 10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology, Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int.Conf. on IPLAFUN'11

SP - 127

EP - 131

BT - 10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11

T2 - 10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11

Y2 - 20 February 2011 through 22 February 2011

ER -

Vorobiev Y, Vieira V, Ribeiro P, Gorley V, Horley P, González-Hernández J et al. Energy spectra of an electron in a pyramid-shaped quantum dot in effective mass approximation with even mirror boundary conditions. In 10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology,Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int. Conf. on IPLAFUN'11. 2011. p. 127-131. (10th WSEAS International Conference on EHAC'11 and ISPRA'11, 3rd WSEAS Int. Conf. on Nanotechnology, Nanotechnology'11, 6th WSEAS Int. Conf. on ICOAA'11, 2nd WSEAS Int.Conf. on IPLAFUN'11).

Energy spectra of an electron in a pyramid-shaped quantum dot in effective mass approximation with even mirror boundary conditions

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Keywords

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