Semiconductor quantum wells with BenDaniel–Duke boundary conditions: approximate analytical results. (6th December 2016)

• Record Type: Journal Article
• Authors: Barsan, Victor; Ciornei, Mihaela-Cristina
• Is Part Of: European journal of physics. Volume 38:Number 1(2017:Jan.)
• Publication Date: 2016-12-06
• Subjects: semiconductor heterojunctions -- quantum wells -- BenDaniel–Duke boundary conditions -- type I and type II semiconductors; Physics -- Periodicals; Physics -- Study and teaching (Higher) -- Europe -- Periodicals; 530
• DOI: 10.1088/0143-0807/38/1/015407
• Languages: English
• ISSNs: 0143-0807

Abstract

Abstract: The Schrödinger equation for a particle moving in a square well potential with BenDaniel–Duke boundary conditions is solved. Using algebraic approximations for trigonometric functions, the transcendental equations of the bound states energy are transformed into tractable, algebraic equations. For the ground state and the first excited state, they are cubic equations; we obtain simple formulas for their physically interesting roots. The case of higher excited states is also analysed. Our results have direct applications in the physics of type I and type II semiconductor heterostructures.