Multiscale Computation and Analysis for Schr(o)dinger-Poisson System in Heterogeneous Materials

来源 :Second China-Brazil Conference on Scientific Computing(北京第二届 | 被引量 : 0次 | 上传用户:cnyy20
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  In this talk, we discuss the multiscale computation for Schr(")odinger-Poisson system arising from the electronic properties of semiconductors such as quantum wells, wires and dots, and CMOS transistor.We first introduce the Schr(o)dinger equations with the effective mass approximation which has been particularly successful in the case of heterostructures.Combining Allaires work (cf.[?]) and our result (cf.[?, ?]), we give a interpretation why the effective mass approximation is very successful for calculating the band structures of semiconductor nanostructures in the vicinity of Γ point, from the viewpoint of mathematics.Second, we analyze the relationship between microscopic Maxwells equations and macroscopic Maxwells equations.Furthermore, we discuss mathematical modeling of electromagnetics at nano-scale and offer an explanation as to why Schr(o)dinger-Poisson equations and Maxwell-Schr(o)dinger equations have been widely used to semiconductor nanostructures.Third, the multiscale method or Schr(o)dinger-Poisson system in heterogeneous materials is presented.Numerical simulations are carried out to validate the theoretical results.Finally, some unsolved problems are advanced.
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