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PAMELA: An Open-Source Software Package for Calculating Nonlocal Exact Exchange Effects on Electron Gases in Core-Shell Nanowires
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/usagiComment: Accepted by AIP Advance
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