Implementation and Application of
Advanced Density Functionals
Michael Christopher Gibson
A thesis submitted for the degree of
Doctor of Philosophy
Department of Physics
University of Durham
Density functional theory (DFT) is a method of effectively solving the
many-electron Schrödinger equation, enabling the properties
of condensed matter systems to be calculated from first principles.
With the commonly used local density approximation (LDA), and generalised
gradient approximations (GGAs), to the exchange correlation functional,
it is currently
possible to perform calculations on systems containing several
hundred atoms. The accuracy of such calculations depends on the system
under study and on which particular properties one wishes to calculate.
The use of more advanced functionals has the potential to improve
accuracy, at the expense of greater computational demand. In this work
we use the LDA to calculate certain properties of GaN, such as geometry,
band structure, and surface properties, including the reconstruction of
GaN surfaces under the presence of hydrogen. We then describe our
computational implementation of advanced density functionals, including
screened exchange (sX-LDA), Hartree-Fock (HF), and exact exchange (EXX),
within an efficient,
fully parallel, plane wave code. The implementation of sX-LDA and HF
is used to calculate
band structure properties of Si, GaN, and other simple semiconductors, and it
is found that sX-LDA can improve results significantly beyond the
LDA. We also derive and implement the theory that allows one to calculate
the contribution to the stress tensor from exchange and correlation when
using these functionals, and demonstrate this with some simple
test cases. Finally, we introduce some new
theoretical ideas that may
pave the way for yet more accurate density functionals in the future.
The work presented here has contributed to the following publications:
- Screened Exchange Stress Tensor in Density Functional Theory,
M. C. Gibson,
S. Brand, S. J. Clark, Phys. Rev. B. 73, 125120 (2006).
- Screened Exchange Calculations of Semiconductor Band Structures,
M. C. Gibson, S. J. Clark, S. Brand, R. A. Abram, AIP Conf. Proc. 772, 1125 (2005).
calculations of reconstructions of GaN(0001) surfaces
involving N, Al, Ga, In, and As atoms,
V. Timon, S. Brand, S. J. Clark,
M. C. Gibson,
R. A. Abram, Phys. Rev. B 72, 035327 (2005).
- Defect Energy Levels in Hf,
High-Dielectric-Constant Gate Oxide,
A. K. Xiong, J. Robertson, M. C. Gibson,
S. J. Clark, App. Phys. Lett. 87, 183505 (2005).
The work presented here was undertaken within the Department of Physics at
the University of Durham between August 2002 and August 2005. I confirm
that no part of this work has previously been submitted for a degree at
this or any other institution and, unless otherwise stated, it is the
original work of the author.
Michael C. Gibson
The copyright of this thesis rests with the author. No quotation, figure,
or any other part of it should be published in any format, including
electronic and the Internet, without his prior written consent. All
information derived from this thesis must be acknowledged appropriately.
First and foremost I would like to thank my supervisor Stewart Clark for his
help, advice, curry, and malt whisky over the past few years. Thanks also to my co-supervisor
Stuart Brand, head of research group Richard Abram, and everyone else who has
been involved with the Durham condensed matter theory group during my time here.
In particular I would like to thank Ian Bolland for helping learn the basics
of Linux when I arrived, Paul Tulip for his entertaining office rants, and Dom Jochym for
some Linux-related tips that have proved very useful in writing this thesis.
Outside of work I would like to thank my girlfriend and my family for their constant
support and encouragement, without which the completion of this work would not have