A Nested Dissection Approach to Modeling Transport in Nanodevices: Algorithms and Applications

TL;DR

This paper introduces a novel graph partitioning-based method for calculating charge density in nanoscale quantum devices, offering reduced computational complexity and faster performance compared to traditional recursive Green's function techniques.

Contribution

It presents a new approach leveraging nested dissection algorithms to efficiently model quantum transport in nanodevices with open boundary conditions.

Findings

Significant speed-up over recursive Green's function methods.

Successfully applied to quantum well superlattice and carbon nanotube.

Handles realistic open boundary conditions with full self-energy matrices.

Abstract

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 paper, we present an approach to calculate the charge density in nanoscale devices, within the context of the non equilibrium Greens function approach. Our approach exploits recent advances in using an established graph partitioning approach. 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. Our method to calculate the electron density has a reduced complexity compared to the established recursive Greens function approach. As an example, we apply our algorithm to a quantum well superlattice and a carbon nanotube, which are represented by a continuum and tight binding Hamiltonian respectively, and demonstrate significant speed up over the recursive method.