Toward Accurate and Efficient Computational Screening of the Electronic Structure and Band Gaps

81 Pages·2017·2.19 MB·English

by  Linda Grabill

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Linda Grabill
Western Washington University, [email protected]
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Grabill, Linda, "Toward Accurate and Efficient Computational Screening of the Electronic Structure and
Band Gaps of Semiconductors" (2016). WWU Graduate School Collection. 531.
https://cedar.wwu.edu/wwuet/531
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Toward Accurate and Efficient Computational
Screening of the Electronic Structure and
Band Gaps of Semiconductors

By

Linda Grabill

Accepted in Partial Completion
of the Requirements for the Degree
Master of Science

Kathleen L. Kitto, Dean of the Graduate School

ADVISORY COMMITTEE

Chair, Dr. Robert Berger

Dr. Tim Kowalczyk

Dr. Marc Muniz
MASTER’S THESIS

In presenting this thesis in partial fulfillment of the requirements for a master’s degree at
Western Washington University, I grant to Western Washington University the non-
exclusive royalty-free right to archive, reproduce, distribute, and display the thesis in any
and all forms, including electronic format, via any digital library mechanisms maintained by
WWU.

I represent and warrant this is my original work, and does not infringe or violate any
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third party copyrighted material included in these files.

I acknowledge that I retain ownership rights to the copyright of this work, including but
not limited to the right to use all or part of this work in future works, such as articles or
books.

Library users are granted permission for individual, research and non-commercial
reproduction of this work for educational purposes only. Any further digital posting of
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Any copying or publication of this thesis for commercial purposes, or for financial gain,
is not allowed without my written permission.

Linda Grabill
July 26th, 2016
Toward Accurate and Efficient Computational
Screening of the Electronic Structure and
Band Gaps of Semiconductors

A Thesis
Presented to
The Faculty of
Western Washington University

In Partial Fulfillment
Of the Requirements for the Degree
Master of Science

by
Linda Grabill
July 2016
Abstract

With increasing population, growing energy demands, and environmental concerns
the search for greener energy resources has intensified in recent decades. For example, in the
ongoing effort to harness solar energy, researchers have worked to identify and optimize the
efficiency of semiconductors beyond traditional silicon photovoltaic materials.
In the development of new materials, synthetic chemists and materials scientists often
look to computational chemistry to guide and understand experiments. In the case of
semiconductors for solar energy conversion, this includes calculations of electronic band
structure and band gap. The most precise computational approaches, such as density
functional theory (DFT) are both time consuming and demanding of computer resources.
Less computationally demanding methods, such as the semi-empirical extended Hückel (eH)
method, are generally seen as less quantitatively predictive. In this work, we show that the
eH electronic band structures of three prototypical semiconductors -- CdSe, SrTiO , and TiO
3 2
-- can be brought into close quantitative agreement with DFT when the eH elemental
parameters are systematically calibrated. We show that it is possible to simultaneously
calibrate parameters for two compounds, suggesting that our approach can in the future be
used to quickly and transferably screen and predict the electronic properties of a wide range
of novel materials.
iv
Acknowledgments
My academic journey at Western Washington University, both as an undergraduate
and a graduate student, has exceeded every expectation. I have been on the receiving end of
care and compassion as peers, supervisors, and the University itself helped me through the
death of one family member and the near death of my father along with my own litany of
physical issues. There are no words to satisfactorily express my gratitude or how deeply
touched I am by it all, especially that throughout, I have been pushed beyond my comfort
zones and encouraged to explore even when outcomes were uncertain.
I would like to specifically acknowledge my advisor, Dr. Robert F. Berger for his
interminable encouragement, ceaseless support and infinite patience. There is an adage
regarding knowing one’s own strengths and weaknesses; being aware my enthusiasm can be
both an asset and a hindrance Dr. Berger provided the gentle guidance and reminders to give
me the focus and direction necessary for the completion of a project of this complexity. He
has helped me develop skills I thought were beyond my abilities and helped lay the
foundation in my development as a scientist and a teacher. I cannot thank him enough.
My sincerest appreciation to my thesis committee members: Dr.Tim Kowalczyk, Dr.
Marc Muniz, and Dr. Mark Bussell. Your time and commitment to detail made completion
of this project possible and enjoyable.
To Amy Cully, Dr. Spencer Berger, Dr. Elizabeth Raymond and Dr. Marc Muniz, I
and my future students all thank your guidance in teaching. It is your approaches I try most
to replicate. You have taught me the gift of perspective and passion. Thank you.
To my family who has learned to translate what thirty more minutes truly means.
My academic endeavors have been more time consuming and stressful than any of us could
have anticipated. You were and remain my rocks. There were many times when you had
more faith in my abilities than I did. You have been willing to go the extra mile at home
when I could not. I must be clear though mom, Sheldon Cooper and I study very different
things.
Last, but certainly not least, to my host of doctors, surgeons, and physical therapists.
You have made it possible for me to accomplish things far beyond anything thought possible
as few as five or six years ago. I now am preparing to return as an Adjunct Professor to a
school I was only barely able to walk across a very short ten years ago, an impossibility if not
for the care and support of my “medical posse.” Were it not for your skills and
determination, none of this would be possible. You have given me the opportunity to live a
life I never could have predicted or imagined. Thank you to the surgeons, Dr’s. Jon White,
Way Yin and Richard Rooney, Dr. Stacia Smith, ARPN Diane Kutzke and a very special
thank you to Dr. Jay Smith and the freshly minted Dr. JR Smith along with the talented PTA
Brenna Kentch and the always helpful, friendly and all things good and happy staff, the long
suffering wife of Jay - Sharon Smith, and their sons Josh and Jordan. Not to forget the rest of
the staff who have tolerated the phone calls, badgering and noise in the lobby. You have all
made this accomplishment possible.
In memoriam of Lee and your kind words and gentle smile. You are missed.
v
Table of Contents
Abstract ................................................................................................................................... iv
Acknowledgment ......................................................................................................................v
List of Figures ......................................................................................................................viii
List of Tables .......................................................................................................................... x
1 Introduction ......................................................................................................................1
1.01 Energy consumption and alternatives .............................................................................1
1.02 Semiconductors ...............................................................................................................2
1.02.1 Band gaps and applications in solar energy conversion ..............................................2
1.02.2 Band structures ............................................................................................................4
1.03 Computational chemistry ................................................................................................5
1.04 Thesis Goals ....................................................................................................................6
1.05 Previous work .................................................................................................................7
2 Methods .............................................................................................................................9
2.01 Density functional theory calculations............................................................................9
2.02 Extended Hückel calculations .......................................................................................10
2.03 Parameter calibration programs ....................................................................................13
2.04 Optimization algorithms ...............................................................................................13
3 Parameter calibration programs ...................................................................................14
3.01 Overview .......................................................................................................................14
vi
3.02 Reading VASP files ......................................................................................................14
3.03 Initializing our parameter calibration program .............................................................17
3.04 Calculating a RMSD .....................................................................................................18
3.05 Optimizing the extended Hückel input parameters .......................................................18
3.06 Plotting band structures.................................................................................................19
3.07 Dual optimization..........................................................................................................20
4 Results ..............................................................................................................................22
4.01 Cadmium selenide .........................................................................................................22
4.02 Strontium titanate ..........................................................................................................28
4.03 Titanium dioxide ...........................................................................................................33
4.04 Dual optimization, SrTiO and TiO .............................................................................36
3 2
5 Conclusion .......................................................................................................................39
I. References ........................................................................................................................40
Appendix ..................................................................................................................................44
A. Initial Single compound optimization in Python3 ........................................................44

vii
List of Figures

Figure 1: An illustration of the contrast in electronic structure between Si atoms (left) and
crystalline Si (right). Atomic orbitals lie at discrete energies, while electronic bands in solids
lie at a continuum of energies, with filled and unfilled bands separated by a band gap. .......... 3

Figure 2: The visible portion of the electromagnetic spectrum in terms of wavelength (nm)
and energy (eV)......................................................................................................................... 4

Figure 3: Electronic band structure of TiO , computed using density functional theory. ....... 5
2

Figure 4: Sample CONTCAR file. ....................................................................................... 15

Figure 5: Sample eH (YAeHMOP) input file for the electronic band structure of SrTiO . 16
3

Figure 6: Sample IBZKPT file for the electronic band structure of (TiO ) using
2
automatically generated k-point mesh. ................................................................................... 16

Figure 7: Sample output for . ................................................ 19
tracking_the_changes

Figure 8: Sample band diagram for SrTiO generated by graph_vasp. ................................ 20
3

Figure 9: CdSe (Wurtzite Structure): Cd, green atoms; Se, purple atoms. ............................ 22

Figure 10: CdSe band diagram with default eH elemental parameters. DFT bands are red
and eH bands are blue. ............................................................................................................ 23

Figure 11: CdSe band diagram with calibrated Cd and Se s and p parameters. DFT bands are
red and eH bands are blue. ...................................................................................................... 24

Figure 12: CdSe band diagram, in which Cd includes valence s, p, and d orbitals, while Se
includes valence s and p orbitals. DFT bands are red and eH bands are blue. ....................... 25

Figure 13: CdSe band diagram, in which Cd includes valence s and p orbitals, while Se
includes valence s, p, and d orbitals. DFT bands are red and eH bands are blue. .................. 26

Figure 14: CdSe band diagram, in which Cd includes valence s and p orbitals, Se includes
valence s, p, and d orbitals, and K is allowed to vary. DFT bands are red and eH bands are
blue. ......................................................................................................................................... 27

Figure 15: SrTiO structure: Sr, green atoms; Ti, blue atoms; and O, red atoms. ................. 29
3

Figure 16: SrTiO band diagram with default elemental parameters. DFT bands are red and
3
eH bands are blue. ................................................................................................................... 30

viii
Figure 17: SrTiO band diagram with eH elemental parameters such that only Ti has valence
3
d orbitals. DFT bands are red and eH bands are blue. ........................................................... 31

Figure 18: SrTiO band diagram with eH elemental parameters optimized, including Sr
3
valence 4d orbitals. DFT bands are red and eH bands are blue. ............................................ 32

Figure 19: SrTiO band diagram with eH elemental parameters optimized and K allowed to
3
vary, including Sr valence 4d orbitals. DFT bands are red and eH bands are blue. .............. 33

Figure 20: Rutile structure of TiO . Blue atoms are Ti and red atoms are O. ...................... 34
2

Figure 21: TiO band diagram with default eH elemental parameters. DFT bands are red
2
and eH bands are blue. ............................................................................................................ 35

Figure 22: TiO band diagram with eH elemental parameters optimized. DFT bands are red
2
and eH bands are blue. ............................................................................................................ 35

Figure 23: SrTiO band diagram, K=1.75. DFT bands are red and eH bands are blue. ....... 37
3

Figure 24: TiO band diagram, K=1.75. DFT bands are red and eH bands are blue. ........... 37
2

Figure 25: SrTiO band diagram after a simultaneous calibration of SrTiO and TiO ,
3 3 2
K=1.79. DFT bands are red and eH bands are blue. .............................................................. 38

Figure 26: TiO band diagram after a simultaneous calibration of SrTiO and TiO , K=1.79.
2 3 2
DFT bands are red and eH bands are blue. ............................................................................. 38

ix