# Scalable Atomistic Simulations of Quantum Electron Transport using Empirical Pseudopotentials

## TL;DR

This paper introduces a scalable, plane-wave-based atomistic simulation method for quantum electron transport, achieving high accuracy and efficiency in modeling large nanostructures like graphene transistors.

## Contribution

It develops a novel plane-wave approach with a partition-of-unity method, matching tight-binding performance while enabling large-scale simulations on personal computers.

## Key findings

- Achieves 100x speedup over previous plane wave methods.
- Reduces memory requirements significantly.
- Successfully simulates a 2000-atom graphene transistor.

## Abstract

The simulation of charge transport in ultra-scaled electronic devices requires the knowledge of the atomic configuration and the associated potential. Such "atomistic" device simulation is most commonly handled using a tight-binding approach based on a basis-set of localized orbitals. Here, in contrast to this widely used tight-binding approach, we formulate the problem using a highly accurate plane-wave representation of the atomic (pseudo)-potentials. We develop a new approach that separately deals with the intrinsic Hamiltonian, containing the potential due to the atomic configuration, and the extrinsic Hamiltonian, related to the external potential. We realize efficient performance by implementing a finite-element like partition-of-unity approach combining linear shape functions with Bloch-wave enhancement functions. We match the performance of previous tight-binding approaches, while retaining the benefits of a plane wave based model. We present the details of our model and its implementation in a full-fledged self-consistent ballistic quantum transport solver. We demonstrate our implementation by simulating the electronic transport and device characteristics of a graphene nanoribbon transistor containing more than 2000 atoms. We analyze the accuracy, numerical efficiency and scalability of our approach. We are able to speed up calculations by a factor of 100 compared to previous methods based on plane waves and envelope functions. Furthermore, our reduced basis-set results in a significant reduction of the required memory budget, which enables devices with thousands of atoms to be simulated on a personal computer.