Energies and wave functions of an off-centre donor in hemispherical quantum dot: Two-dimensional finite difference approach and ritz variational principle

详细信息    查看全文

• 作者：Soukaina Nakra Mohajer^a ; El Hassan El Harouny^a ; Asmaa Ibral^b ; ^c ; Jamal El Khamkhami^a ; El Mahdi Assaid^b ; ^c ; ^{eassaid@yahoo.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：One-dimension finite difference approach ; Two-dimension finite difference approach ; Ritz variational principle ; Donor impurity ; Hemispherical quantum dot
• 刊名：Physica B: Physics of Condensed Matter
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：497
• 期：Complete
• 页码：51-58
• 全文大小：1217 K

文摘

Eigenvalues equation solutions of a hydrogen-like donor impurity, confined in a hemispherical quantum dot deposited on a wetting layer and capped by an insulating matrix, are determined in the framework of the effective mass approximation. Conduction band alignments at interfaces between quantum dot and surrounding materials are described by infinite height barriers. Ground and excited states energies and wave functions are determined analytically and via one-dimensional finite difference approach in case of an on-center donor. Donor impurity is then moved from center to pole of hemispherical quantum dot and eigenvalues equation is solved via Ritz variational principle, using a trial wave function where Coulomb attraction between electron and ionized donor is taken into account, and by two-dimensional finite difference approach. Numerical codes developed enable access to variations of donor total energy, binding energy, Coulomb correlation parameter, spatial extension and radial probability density with respect to hemisphere radius and impurity position inside the quantum dot.