Numerical Exploration of Isolated GaAs-AlGaAs Quantum Well

2024
ISBN: 978-3-031-53815-5
Verlag: Springer Nature Switzerland

Buch, Englisch, 91 Seiten, Format (B × H): 173 mm x 246 mm, Gewicht: 378 g

Reihe: Synthesis Lectures on Engineering, Science, and Technology

This book begins with the eigenvalue equation of energy and presents calculation of the energy spectrum of GaAs-AlGaAs Quantum Well using finite difference method and knowledge of potential energy profile, without using expressions for eigenfunctions, continuity of eigenfunctions, or their spatial derivatives at the two abrupt potential steps. The authors find that the results are almost the same as those obtained by solving numerically using regula falsi method, and transcendental equations that are obeyed by the energy levels, where the transcendental equations are obtained by requiring continuity of eigenfunctions and of their spatial derivatives at the two potential steps. Thus, this book confirms that it is possible to numerically calculate the energy spectrum of Quantum Well by the finite difference method when it is not correct or when it is not possible to use continuity of eigenfunctions and their spatial derivatives at the two abrupt potential steps. The authors also showthat it is possible to use the finite difference method in cases where the potential steps are non-abrupt. The book demonstrates this by calculating the energy spectrum of isolated parabolic Quantum Well of finite depth using finite difference method.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Talukder, Urmi

Chowdhury, Sujaul

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Materialwissenschaft: Biomaterialien, Nanomaterialien, Kohlenstoff
• Naturwissenschaften Physik Angewandte Physik
• Naturwissenschaften Physik Elektromagnetismus Halbleiter- und Supraleiterphysik
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Technische Wissenschaften Technik Allgemein Nanotechnologie

Inhaltsverzeichnis

Background on Microelectronics.- Background on Semiconductor Nanostructure Physics.- Numerical Calculation of Energy Spectrum of GaAs-AlGaAs Quantum Well Having Abrupt Potential Steps Using Regula Falsi Method.- Numerical calculation of Energy Spectrum of GaAs-AlGaAs Quantum Well Having Abrupt Potential Steps Using Finite Difference Method.- Numerical Calculation of Energy Spectrum of Parabolic Quantum Well of Finite Depth Using Finite Difference Method.

Über Autor(innen)

Sujaul Chowdhury, Ph.D., is a Professor in the Department of Physics at Shahjalal University of Science and Technology. He received his B.Sc. and M.Sc. in Physics from Shahjalal University of Science and Technology, before earning his Ph.D. at The University of Glasgow in 2001. He is the author of many books, including and

Urmi Talukder is an M.S. student in Department of Physics at Shahjalal University of Science and Technology.