Numerical Exploration of Isolated GaAs-AlGaAs Quantum Well (Synthesis Lectures on Engineering, Science, and Technology)

Chowdhury, Sujaul/ Talukder, Urmi

Springer International Publishing AG（2025/04発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 91 p.
• 言語 ENG
• 商品コード 9783031538186

Full Description

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.

Contents

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.