The Generalized Scattering Matrix Approach: An Efficient Technique for Modeling Quantum Transport in Relatively Large and Heavily Doped Structures
Over the past few years, a number of theoretical techniques have appeared in the literature for simulating phase-coherent electron transport through disordered meso-scopic structures. Notable among these are the Green’s function methods  and transfer matrix approaches . In this paper, we discuss an alternate technique the generalized scattering matrix approach — which is ideal for studying transport through relatively large and heavily doped structures. Unlike the Green’s function method which has a computational cost proportional to (NL)4 and a storage requirement proportional to (NL)2 (N is the number of dopants or scattering centers in the structure and L is the structure’s length), the scattering matrix technique has a computational cost proportional to (NL)3 and a storage requirement proportional to (NL) . The reduced storage requirement is a highly desirable feature in a supercomputing environment since it decreases the number of small page faults and input/output operations which then reduces the real time of computation1. Consequently, the scattering matrix technique is optimal for treating those problems that require simulating transport in relatively large and heavily doped structures.
KeywordsLocalization Length Anderson Localization Evanescent Mode Wide Structure Dope Structure
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