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Abstract
This thesis is concerned with the modeling of electronic properties of nanoscale
devices. In particular the computational aspects of calculating the transmission
and currentvoltage characteristics of LandauerBüttiker twoprobe systems are
in focus. To begin with, the main existing methods are described in detail and
benchmarked. These are the Green’s function method and the wave function
matching method. The methods are subsequently combined in a hybrid scheme
in order to benefit from a common formalism.
The most time demanding stages of common electronic transport calculations
are identified. For systems of more than about a hundred atoms, two
specific tasks stand out; the evaluation of selfenergy matrices to describe the
coupling between the electrodes and the device, and the solution of the central
region Schrödinger equation either by matrix inverse of by solving a system of
linear equations. In this work the objective is to develop new efficient algorithms
for these tasks in order to model nanoscale systems of larger size in the future.
The starting point of the new methods is the combined formalism of the Green’s
function and wave function matching methods.
The first new algorithm described is for the calculation of the block tridiagonal
matrix inverse of a block tridiagonal matrix in O(N) operations. This
algorithm also leads to an optimal evaluation of the frequently used Caroli transmission
formula. A modified wave function matching scheme is then developed
which allows for a significant reduction in the cost of the selfenergy matrix
calculations when combined with an iterative eigensolver. Finally, such an iterative
eigensolver is developed and implemented based of a shiftandinvert
Krylov subspace approach. The method is applied to a selection of nanoscale
systems and speedups of up to an order of magnitude are achieved.
Original language  English 

Publication status  Published  Jul 2008 

Series  DTU Compute PHD 

ISSN  09093192 
Bibliographical note
IMMPHD2008195Fingerprint
Dive into the research topics of 'Computational aspects of electronic transport in nanoscale devices'. Together they form a unique fingerprint.Projects
 1 Finished

Scientific Computing and Parallel Algorithms in Computational Nano science
Sørensen, H. H. B., Hansen, P. C., Stokbro, K., Sørensen, M. P., Darve, E., Wacker, A. & Skelboe, S.
15/04/2005 → 02/07/2008
Project: PhD