Predicting the Electronic Properties of 3D, Million-atom Semiconductor nanostructure Architectures

Jack Dongarra ; Stanimire Tomov

关键词: ACCURACY;    ALGORITHMS;    ARCHITECTURE;    DESIGN;    EIGENVALUES;    ENERGY GAP;    NANOSTRUCTURES;    PHYSICS;    RELIABILITY;    TRANSPORT computational nano-technology;    electronic structure;    preconditioned conjugate gradients;    bulk band;    quantum dots;    parallel eigenvalue solvers;    block method;   

DOI  :  10.2172/1036499
RP-ID  :  DOE/ER25584-5
PID  :  OSTI ID: 1036499
Others  :  TRN: US201208%%869

学科分类：纳米科学和纳米技术

美国|英语

来源: SciTech Connect

【 摘 要 】

This final report describes the work done by Jack Dongarra (University Distinguished Professor) and Stanimire Tomov (Research Scientist) related to the DOE project entitled Predicting the Electronic Properties of 3D, Million-Atom Semiconductor Nanostructure Architectures. In this project we addressed the mathematical methodology required to calculate the electronic and transport properties of large nanostructures with comparable accuracy and reliability to that of current ab initio methods. This capability is critical for further developing the field, yet it is missing in all the existing computational methods. Additionally, quantitative comparisons with experiments are often needed for a qualitative understanding of the physics, and for guiding the design of new nanostructures. We focused on the mathematical challenges of the project, in particular on solvers and preconditioners for large scale eigenvalue problems that occur in the computation of electronic states of large nanosystems. Usually, the states of interest lie in the interior of the spectrum and their computation poses great difficulties for existing algorithms. The electronic properties of a semiconductor nanostructure architecture can be predicted/determined by computing its band structure. Of particular importance are the 'band edge states' (electronic states near the energy gap) which can be computed from a properly defined interior eigenvalue problem. Our primary mathematics and computational challenge here has been to develop an efficient solution methodology for finding these interior states for very large systems. Our work has produced excellent results in terms of developing both new and extending current state-of-the-art techniques.