Abstract
AbstractWhen the effective mass approximation is used for analysis of electrons bound in a quantum well, the envelope function generally is not continuous at the heterojunction. The boundary condition at the junction is expressed in terms of the transfer matrix. In this paper, an analysis method based on the finite‐element formulation is proposed for electrons bound in a quantum well made of arbitrary materials. It is shown that by using 3rd‐order Hermitian line elements as the approximation functions, the continuities of the envelope function and its derivative are ensured outside the heterojunction, and that introduction of the transfer matrix becomes possible. It is also shown that the problem becomes an asymmetric generalized eigenvalue problem by means of this formulation. As numerical examples, rectangular quantum wells are analyzed in the cases where the envelope function, and its derivative divided by the effective mass, are continuous at the heterojunction (GaAs/A1GaAs quantum well) where also the function and its derivative are discontinuous (InAs/GaSb quantum well). The validity of the calculations is confirmed by comparison with the analytical solutions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Electronics and Communications in Japan (Part II: Electronics)
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.