Open Access Nano Express

Weak and strong confinements in prismatic and cylindrical nanostructures

Yuri V Vorobiev1*, Bruno Mera2, Vítor R Vieira2, Paul P Horley3 and Jesús González-Hernández3

Author affiliations

1 CINVESTAV-Querétaro, Libramiento Norponiente 2000, Fracc. Real de Juriquilla, Querétaro, QRO, 76230, Mexico

2 Centro de Física das Interacções Fundamentais, Instituto Superior Técnico, Universidade Técnica de Lisboa, Avenida Rovisco Pais, Lisbon, 1049-001, Portugal

3 CIMAV Chihuahua/Monterrey, 120 Avenida Miguel de Cervantes, Chihuahua, CHIH, 31109, Mexico

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Citation and License

Nanoscale Research Letters 2012, 7:371  doi:10.1186/1556-276X-7-371

Published: 5 July 2012


Cylindrical nanostructures, namely, nanowires and pores, with rectangular and circular cross section are examined using mirror boundary conditions to solve the Schrödinger equation, within the effective mass approximation. The boundary conditions are stated as magnitude equivalence of electron's Ψ function in an arbitrary point inside a three-dimensional quantum well and image point formed by mirror reflection in the walls defining the nanostructure. Thus, two types of boundary conditions - even and odd ones - can be applied, when Ψ functions in a point, and its image, are equated with the same and the opposite signs, correspondingly. In the former case, the Ψ function is non-zero at the boundary, which is the case of a weak confinement. In the latter case, the Ψ function vanishes at the boundary, corresponding to strong quantum confinement. The analytical expressions for energy spectra of electron confined within a nanostructure obtained in the paper show a reasonable agreement with the experimental data without using any fitting parameters.