| Modeling nanoscale devices quantum mechanically is a computationally challenging problem where new methods to solve the underlying equations are in a dire need.;In this Ph.D. work, we design and implement an efficient and high quality numerical algorithm to solve Green's functions, within the framework of non-equilibrium Green's function (NEGF) calculation, which is the most accurate approach in electronic transport simulation. Our approach exploits and extends a recent advance in using an established graph partitioning method, namely the nested dissection. The developed method has the capability to handle open boundary conditions that are represented by full self-energy matrices required for realistic modeling of nanoscale devices. We demonstrate that our method has a reduced complexity and significant speedup compared to the state-of-the-art recursive Green's function (RGF) approach across a variety of two-dimensional systems and, more important, three-dimensional structures including the traditional silicon nanowire, emerging graphene based multilayer devices, and DNA molecules.;As a novel application of the proposed simulator, we investigate the tunneling transport properties of heterostructures consisting of a few atomic layers thick hexagonal Boron Nitride (hBN) film sandwiched between armchair edged graphene nanoribbon electrodes. By incorporating our efficient Green's function solver, the modeled device ranges from a small system with 6,000 atoms to experimental feasible sizes up to 70,000 atoms. We show a gate-controllable vertical transistor exhibiting strong negative differential resistance (NDR) effect with multiple resonant peaks, which originate from two distinct mechanisms depending on the gate and applied bias in the same device. We perform a scaling analysis of the NDR feature as a function of the system size and gain instructive insights for future theoretical and experimental investigations.;To convey more experimentally realistic simulation, we incorporate (i) angular misorientation between multilayer heterostructure, which inducing a distinct resonant mechanism depending on both gate bias and twisting angle; (ii) electron-phonon scattering decoherence mechanism, which successfully captures the current NDR peaks degradation observed in room-temperature experiments. The NDR feature with multiple resonant peaks, combined with the ultrafast tunneling speed provides prospect for the graphene-hBN-graphene heterostructure in the high-performance electronics. |
