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|Title: ||The accuracy of filtered basis functions for the first principles modelling of defects in semiconductors|
|Authors: ||Shrif, Fadil Ezzedin Irhoma|
|Issue Date: ||2013 |
|Publisher: ||Newcastle University|
|Abstract: ||This work presents the results of calculations using filtered basis functions performed
with the ab initio modelling program (AIMPRO). The filtration method works by projecting
out (filtering) components of a reference basis function that are not required
for a description of the occupied states, thereby producing functions that are localised
in energy. This leads to a significant reduction in the number of functions that are
needed. It is demonstrated that when studying diamond, silicon and defects in these
materials, the use of filtered basis sets using just four basis functions per atom can
achieve a comparable accuracy to conventional calculations that use 30–40 basis functions.
This enables a massive increase in computational efficiency that could have far
reaching consequences for first principles modelling calculations.
The accuracy of the filtration method is first examined for the bulk materials
diamond and silicon, in which the energy, lattice constant, bulk modulus and band
structure are studied. It is shown that the filtration approximation applied with an
efficient spatial cut-off is able to reproduce current calculated values for these to a
very high degree of accuracy.
A study of the energies of various reconstructed surfaces in diamond and silicon is
then presented. It is first demonstrated that the AIMPRO modelling software without
filtration reproduces previous published values of surface energies to within about 100
meV per 1x1 surface cell, with this difference being related to different choices for the
pseudo-potential and other details of the calculation. It is also demonstrated that
changes of this degree also occur when changing the exchange-correlation functional
used to model the surface. In contrast, the use of filtered basis sets changes these
energies by only 1–2 meV, one hundred times smaller, indicating the excellence of this
approach and showing that filtered basis calculation with efficient cut-off radii are of
essentially equal quality to those of conventional localised basis functions.
Finally a series of defect structures in diamond is considered, including both native
defects and nitrogen containing defects. Properties studied include formation energies,
binding energies, localised vibrational modes, and hyperfine coupling matrices.
In all these cases it is shown that the filtration method produces results which closely
match those with conventional basis sets and demonstrate that this method has excellent
potential for modelling defecting semiconductor structures in the future. The
asymptotic speed up of two to three orders of magnitude will then enable a new range
of systems with significantly increased size and complexity to be modelled.|
|Description: ||PhD Thesis|
|Appears in Collections:||School of Electrical and Electronic Engineering|
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