Weak and strong confinements in prismatic and cylindrical nanostructures

• Published in: Nanoscale research letters Vol. 7; no. 1; p. 371
• Main Authors: Vorobiev, Yuri V, Mera, Bruno, Vieira, Vítor R, Horley, Paul P, González-Hernández, Jesús
• Format: Journal Article
• Language: English
• Published: New York Springer New York 05-07-2012; BioMed Central Ltd; Springer
• Subjects: Chemistry and Materials Science; Materials Science; Molecular Medicine; Nano Express; Nanochemistry; Nanoscale Science and Technology; Nanotechnology; Nanotechnology and Microengineering; Porous Semiconductors - Science and Technology 2012; Impenetrable Wall; Electrical Anisotropy; Effective Mass Approximation; Wave Vector Component; Strong Confinement
• ISSN: 1556-276X; 1931-7573; 1556-276X
• DOI: 10.1186/1556-276X-7-371

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.