Tight-Binding Models, Their Applications to Device Modeling, and Deployment to a Global Community

Abstract

AbstractTight-binding has become the state-of-the-art for realistically sized nanoscale device modeling. It has been implemented by multiple advanced device modeling research groups in conjunction with multiple quantum transport methodologies. Industry has begun to adopt some of the advanced codes and is beginning to implement company internal versions. Commercial software vendors are adopting the methodologies and are beginning to deploy the approaches into their commercial TCAD products. Intense software development combining tight-binding with the non-equilibrium Green’s function (NEGF) approach and quantum transmitting boundary method (QTBM) for quantum transport began in 1994 at Texas Instruments. Acceptance of NEGF and tight-binding began with wider adoption in about 2004. The past 25 years have resulted in many model advancements, numerical technology development, and physics exploration that is by far too large to be covered here comprehensively. We start by setting forth the requirements for realistic modeling of extended nanoscale devices (Sects. 45.1 and 45.2), which include a full quantum mechanical treatment, atomistic interface treatments, atomistic representations of crystal symmetries, polarization, strain, and bond directions, and embedding into macroscopic fields such as electromagnetic potentials and long-range strain. We then proceed to describe the essential definitions and features for empirical tight-binding (Sect. 45.3). Sections 45.4, 45.5, and 45.6 address numerical issues of tight-binding in terms of transfer matrices, Green’s functions, and parallel scaling. Section 45.7 is dedicated to several applications around quantum dots and nanowires. We highlight million-atom quantum dot simulations and focus on carrier transport though silicon nanowires. We demonstrate how effective masses and bandgaps become design parameters at the nanoscale, how heavy masses are desirable for end-of-roadmap transistors, and how coherent transport assumptions break down. The nanowire simulations can be duplicated by everyone on nanoHUB.org. Section 45.8 highlights the widespread use of tight-binding within nanoHUB applications. Section 45.9 concludes this chapter.KeywordsTight bindingTransportNEGFQuantum transportNon equilibrium green functionsQuantum dotNanowireBandstructureEffective massNanoHUBEducation