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Journal of Computational Electronics
Published in: Journal of Computational Electronics 2/2016

02-01-2016

Nested dissection solver for transport in 3D nano-electronic devices

Authors: Y. Zhao, U. Hetmaniuk, S. R. Patil, J. Qi, M. P. Anantram

Published in: Journal of Computational Electronics | Issue 2/2016

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Abstract

The hierarchical Schur complement method (HSC) and the HSC-extension have significantly accelerated the evaluation of the retarded Green’s function, particularly the lesser Green’s function, for two-dimensional nanoscale devices. In this work, the HSC-extension is applied to determine the solution of non-equilibrium Green’s functions on three-dimensional nanoscale devices. The operation count for the HSC-extension is analyzed for a cuboid device. When a cubic device is discretized with \(N \times N \times N\) grid points, the state-of-the-art recursive Green function (RGF) algorithm takes \(\mathscr {O}(N^7)\) operations, whereas the HSC-extension only requires \(\mathscr {O}(N^6)\) operations. Operation counts and runtimes are also studied for three-dimensional nanoscale devices of practical interest: a graphene-boron nitride-graphene multilayer system, a silicon nanowire, and a DNA molecule. The numerical experiments indicate that the cost for the HSC-extension is proportional to the solution of one linear system (or one LU-factorization) and that the runtime speed-ups over RGF exceed three orders of magnitude when simulating realistic devices, such as a graphene-boron nitride-graphene multilayer system with 40,000 atoms.
previous article Properties of electron transmission through serially connected hexagonal nanorings

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Appendix
Available only for authorised users
Footnotes
1
The block on the diagonal of \(\mathbf {G}^{r}\) for the rightmost layer is the corresponding block in the matrix \(\mathbf {D}^{-1}\).
 
2
In practice, the binary tree is likely to be balanced.
 
3
Any cluster with 2-pairs is partitioned according to a degenerate tree, where each parent node has only one child.
 
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Metadata
Title
Nested dissection solver for transport in 3D nano-electronic devices
Authors
Y. Zhao
U. Hetmaniuk
S. R. Patil
J. Qi
M. P. Anantram
Publication date
02-01-2016
Publisher
Springer US
Published in
Journal of Computational Electronics / Issue 2/2016
Print ISSN: 1569-8025
Electronic ISSN: 1572-8137
DOI
https://doi.org/10.1007/s10825-015-0778-x

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