{"title":"Mathematical Analysis of a Nonparabolic Two-Band Schrödinger-Poisson Problem","authors":"O. Morandi","doi":"10.1080/00411450.2014.886591","DOIUrl":null,"url":null,"abstract":"A mathematical model for the quantum transport of a two-band semiconductor that includes the self-consistent electrostatic potential is analyzed. Corrections beyond the usual effective mass approximation are considered. Transparent boundary conditions are derived for the multiband envelope Schrödinger model. The existence of a solution of the nonlinear system is proved by using an asymptotic procedure. Some numerical examples are included. They illustrate the behavior of the scattering and the resonant states.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"1 1","pages":"133 - 161"},"PeriodicalIF":0.0000,"publicationDate":"2013-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2014.886591","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transport Theory and Statistical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00411450.2014.886591","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
A mathematical model for the quantum transport of a two-band semiconductor that includes the self-consistent electrostatic potential is analyzed. Corrections beyond the usual effective mass approximation are considered. Transparent boundary conditions are derived for the multiband envelope Schrödinger model. The existence of a solution of the nonlinear system is proved by using an asymptotic procedure. Some numerical examples are included. They illustrate the behavior of the scattering and the resonant states.
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