PAMELA: An Open-Source Software Package for Calculating Nonlocal Exact Exchange Effects on Electron Gases in Core-Shell Nanowires

TL;DR

This paper introduces PAMELA, an open-source pseudospectral software for accurately modeling nonlocal exchange effects in electron gases within core-shell nanowires, improving upon traditional methods in efficiency and precision.

Contribution

The paper presents a novel pseudospectral approach and software package that efficiently incorporates nonlocal exchange interactions in electron gas modeling in nanowires, surpassing conventional Schrodinger-Poisson methods.

Findings

Nonlocal exchange effects significantly alter electron level predictions.

PAMELA reduces computational effort compared to finite-element methods.

Critical tunneling depth influences electron gas formation in high-doping regimes.

Abstract

We present a new pseudospectral approach for incorporating many-body, nonlocal exact exchange interactions to understand the formation of electron gases in core-shell nanowires. Our approach is efficiently implemented in the open-source software package PAMELA (Pseudospectral Analysis Method with Exchange & Local Approximations) that can calculate electronic energies, densities, wavefunctions, and band-bending diagrams within a self-consistent Schrodinger-Poisson formalism. The implementation of both local and nonlocal electronic effects using pseudospectral methods is key to PAMELA's efficiency, resulting in significantly reduced computational effort compared to finite-element methods. In contrast to the new nonlocal exchange formalism implemented in this work, we find that the simple, conventional Schrodinger-Poisson approaches commonly used in the literature (1) considerably overestimate the number of occupied electron levels, (2) overdelocalize electrons in nanowires, and (3) significantly underestimate the relative energy separation between electronic subbands. In addition, we perform several calculations in the high-doping regime that show a critical tunneling depth exists in these nanosystems where tunneling from the core-shell interface to the nanowire edge becomes the dominant mechanism of electron gas formation. Finally, in order to present a general-purpose set of tools that both experimentalists and theorists can easily use to predict electron gas formation in core-shell nanowires, we document and provide our efficient and user-friendly PAMELA source code that is freely available at http://alum.mit.edu/www/usagi