Atomic Scale Characterization and First-Principles Studies of Si₃N₄ Interfaces

113 Pages·2011·3.89 MB·English

by  Weronika Walkosz (auth.)

Springer Theses
Recognizing Outstanding Ph.D. Research
For furthervolumes:
http://www.springer.com/series/8790
Aims and Scope
The series ‘‘Springer Theses’’ brings together a selection of the very best Ph.D.
theses from around the world and across the physical sciences. Nominated and
endorsed by two recognized specialists, each published volume has been selected
for its scientific excellence and the high impact of its contents for the pertinent
fieldofresearch.Forgreateraccessibilitytonon-specialists,thepublishedversions
includeanextendedintroduction,aswellasaforewordbythestudent’ssupervisor
explaining the special relevance of the work for the field. As a whole, the series
will provide a valuable resource both for newcomers to the research fields
described, and for other scientists seeking detailed background information on
specialquestions.Finally,itprovidesanaccrediteddocumentationofthevaluable
contributions made by today’s younger generation of scientists.
Theses are accepted into the series by invited nomination only
and must fulfill all of the following criteria
• They must be written in good English.
• The topic of should fall within the confines of Chemistry, Physics and related
interdisciplinary fields such as Materials, Nanoscience, Chemical Engineering,
Complex Systems and Biophysics.
• The work reported in the thesis must represent a significant scientific advance.
• Ifthethesisincludespreviouslypublishedmaterial,permissiontoreproducethis
must be gained from the respective copyright holder.
• They must have been examined and passed during the 12 months prior to
nomination.
• Each thesis should include a foreword by the supervisor outlining the signifi-
cance of its content.
• The theses should have a clearly defined structure including an introduction
accessible to scientists not expert in that particular field.
Weronika Walkosz
Atomic Scale
Characterization and First-
Principles Studies of Si N
3 4
Interfaces
Doctoral Thesis accepted by
the University of Illinois – Chicago,
Chicago, USA
123
Author Supervisors
Dr. WeronikaWalkosz Dr. RobertKlie
ArgonneNational Laboratory Department of Physics
Argonne,IL Universityof Illinois–Chicago
60439 845W.Taylor Street, M/C 273
USA Chicago, IL 60607
e-mail: [email protected] USA
e-mail: [email protected]
Dr. SerdarOgut
Department of Physics
Universityof Illinois–Chicago
845W.Taylor Street, M/C 273
Chicago, IL 60607
USA
e-mail: [email protected]
Dr. JuanC. Idrobo
Materials Science and Technology
Division
OakRidge NationalLaboratory
1 Bethel Valley Rd.
OakRidge,TN 37831
USA
e-mail: [email protected]
ISSN 2190-5053 e-ISSN2190-5061
ISBN 978-1-4419-7816-5 e-ISBN978-1-4419-7817-2
DOI 10.1007/978-1-4419-7817-2
SpringerNewYorkDordrechtHeidelbergLondon
(cid:2)SpringerScience+BusinessMedia,LLC2011
Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten
permissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY
10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in
connection with any form of information storage and retrieval, electronic adaptation, computer
software,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.
Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare
notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject
toproprietaryrights.
Coverdesign:eStudioCalamar,Berlin/Figueres
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Supervisor’s Foreword
This Ph.D. thesis is the result of more than 4 years (mid 2005 through 2009) of
dedicated and meticulous research by Weronika Walkosz at the Physics Depart-
ment of the University of Illinois at Chicago (UIC). During this time, Weronika
worked in two complementary areas of Condensed Matter Physics, experimental
and computational, with two advisors (Klie and Ogut at UIC) and a third super-
visor(JuanIdroboatOakRidgeNationalLaboratory,whowastheactualPIonthe
grant)atdifferentinstitutionsindifferentstatesoftheUnitedStates.Thatshewas
able to do this and finish her thesis successfully is a tribute to her intellectual
capacity, persistence, ambition, and dedication.
Weronika initially started her Ph.D. research in computational materials mod-
eling with one of us (Ogut) and worked, in collaboration with Juan, on first
principles modeling of a variety of systems including SrTiO /GaAs interfaces,
3
elastic properties of InN, and optical absorption spectra of Au clusters. With the
arrival of one us (Klie) at UIC in the Fall of 2006, Weronika became more and
more interested in learning and using electron microscopy techniques, in addition
to her computational studies. As such, one unique aspect of Weronika’s Ph.D.
research, a significant portion (but not all) of which made it into this thesis, is
related to her ability to strive in both computational and experimental platforms.
While many Ph.D. students typically focus on either experimental or theoretical
condensedmatterphysics,Weronikarealizedearlyonthatthecomplexproblemof
the ordering transition in crystal/amorphous interfaces, such as those observed in
Si N /rare-earth oxide and SiO interfaces, can only be understood by using both
3 4 2
theoretical first principles calculations, as well as experimental transmission
electron microscopy. As a result, her thesis describes both theoretical and exper-
imental study of the disorder/ordering transition in structural ceramic materials.
For many years, scientists have studied crystalline amorphous interfaces, since
theyplayanimportantroleinmanytechnologicalmaterials,fromsemiconductors
to structural ceramics and vitrified nuclear waste. In spite of the intense focus, to
date an atomic-scale description of the disorder/ordering transition at ceramic
interfaces has not been well understood and the models developed in Weronika’s
v
vi Supervisor’sForeword
thesis are challengingthe common notionofatomicallyabrupt crystal/amorphous
interfaces.
Inhercomputationalstudies,WeronikamodeledbareSi N surfacesaswellas
3 4
the attachment of oxygen and different rare-earth atoms to these surfaces by uti-
lizing first principles calculations within the framework of density functional
theory(DFT).Sheperformedanexhaustivesearch(testingmorethan350different
interfacial structures), and constructed a phase diagram for oxygenated b-Si N
3 4
surfacesasafunctionofrelevantchemicalpotentialsofoxygenandnitrogen.Her
calculations revealed that the structures commonly observed in Si N /oxide
3 4
interfaces are not energetically favorable, not even in the presence of sub-surface
oxygen or rare-earth elements attached to the surface, challenging both her
experimental and theoretical skills to resolve this puzzle. In the case of a-Si N ,
3 4
Weronika’s calculations revealed that oxygen impurities could diffuse into the
bulk at interstitial positions, and potentially stabilize the a-phase at higher tem-
perature and pressures.
Her experimental work was focused on utilizing state-of-the-art aberration-
corrected scanning transmission electron microscopy (STEM) to characterize
Si N hetero-interfaces and bulk defects. In particular, Weronika focused on
3 4
characterizing, using high-angle annular dark-field imaging (HAADF), annular
dark-field imaging (ABF) and electron energy-loss spectroscopy (EELS), the
structuresshepredictedusingDFTmodeling.Someofherexperimentalresultsare
thefirstofitskindshowingthatthecrystalline/amorphoustransition attheSi N /
3 4
SiO interfacesisnotatomicallyabrupt.Instead,thefirstfewmonolayersofatoms
2
intheamorphousSiO exhibitsomesemi-crystallineordering,inaccordancewith
2
the structures predicted by first-principles modeling. This discovery was made
possible only by the recent development of aberration-corrected STEM at low
accelerationvoltagestoenablethevisualizationofindividualatomseveninbeam
sensitive materials, such as the Si N /SiO interface.
3 4 2
The research described in this thesis is challenging, both experimentally and
theoretically. For modeling hetero-interfaces and determining the lowest energy
configuration and electronic structure of Si N /rare-earth oxide interfaces, large
3 4
super-cells are required, consisting of many atoms. Experimentally, these inter-
facialstructuresareverysensitivetotheelectronbeamandonlyafewsecondsof
exposurecandramaticallyaltertheinterfacialatomic arrangement.Therefore,the
factthatintheendbothfirst-principlesmodelingandexperimentalSTEMimaging
and spectroscopy agree on the interfacial and bulk structures of Si N is an
3 4
amazing tribute to Weronika’s ability as a condensed matter physics graduate
student, who has mastered both the experimental and theoretical aspects of her
project.
WebelievethatWeronika’suniqueabilityofcombiningatomic-levelstructural
characterization with realistic first-principles modeling of interfacial structures
willhavewide-rangingconsequencesonourunderstandingofmanyothersystems.
For example, in dielectric interfaces in semiconductor devices, which are
approachingthequantumlimitofthickness,apartialcrystallineorderingattheSi/
amorphous oxide interface will have significant effects of the device performance
Supervisor’sForeword vii
and influence the end of the roadmap scenario dramatically. The techniques and
methods developed by Weronika in this thesis will aid scientists in the future in
assessing the nature of crystalline/amorphous interfaces and help develop devices
taking advantage of the semi-crystalline ordering discovered in this thesis.
On behalf ofJuan and ourselves,we wouldliketothankWeronika forbeinga
great Ph.D. student to work with and for the opportunity to see her grow into an
exceptional condensed matter physicist who bridges the gap between theoretical
and experimental materials research. We also would like to thank the National
Science Foundation (Grant No. 0605964), in particular Dr. Lynnette D. Madsen,
for supporting this research for the last 4 years, and believing in our ideas of
combining first-principles modeling, aberration-corrected scanning transmission
electron microscopy and electron energy-loss spectroscopy to study the funda-
mental structure-property relationships in ceramic materials. Finally, we are
gratefultoDr.StephenJ.PennycookforhostingWeronikaatOakRidgeNational
Laboratory and providing her with the opportunity of using the STEM group’s
outstanding facilities.
Chicago, August 31, 2010 Serdar Ogut and Robert Klie
Acknowledgments
IwouldliketothankmyadvisorsDr.SerdarOgutandDr.RobertKliefromUIC,
and Dr. Juan C. Idrobo from Vanderbuilt University and Oak Ridge National
Laboratory for their outstanding mentoring during my Ph.D. work. Also, I would
liketothanktheRRCgroup,inparticularDr.AlanNicholls,Dr.Ke-binLow,and
JohnRothwhohavetaughtmevariousmicroscopytechniques.Iamverygrateful
to Dr. Stephen Pennycook and his group at Oak Ridge National Laboratory for
allowingmetousetheirmicroscopyresources.Onapersonalnote,Iwouldliketo
thank my friends from the UIC Physics Department for making my graduate
experience very enjoyable, and my whole family for their love and constant
support. I especially thank my mom.
ix
Contents
1 Silicon Nitride Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Overview of Previous Studies on Si N . . . . . . . . . . . . . . . . . 2
3 4
1.3 Overview of the Present Study . . . . . . . . . . . . . . . . . . . . . . . 3
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Theoretical Methods and Approximations. . . . . . . . . . . . . . . . . . . 11
2.1 Born Oppenheimer Approximation. . . . . . . . . . . . . . . . . . . . . 11
2.2 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Approximations for the Exchange-Correlation
Energy Functional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Periodic Systems: Bloch’s Theorem. . . . . . . . . . . . . . . . . . . . 15
2.5 k-Point Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Plane Waves, Pseudopotentials, and the Projector Augumented
Wave Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.7 Aperiodic Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.8 DFT+U. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Overview of Experimental Tools. . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1 Conventional Transmission Electron Microscope. . . . . . . . . . . 23
3.2 High-Resolution TEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Image Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 Z-contrast Imaging in STEM. . . . . . . . . . . . . . . . . . . . . . . . . 27
3.5 Annular Bright-Field Imaging in STEM . . . . . . . . . . . . . . . . . 29
3.6 Probe Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.7 Electron Energy-Loss Spectroscopy/Energy-Filtered STEM. . . . 33
3.8 Aberration Correctors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.9 Microscopes Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.10 Multivariate Statistical Analysis. . . . . . . . . . . . . . . . . . . . . . . 39
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
xi
xii Contents
4 Structural Energetics of b-Si N ð1010Þ Surfaces . . . . . . . . . . . . . . 45
3 4
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Computational Methods and Parameters . . . . . . . . . . . . . . . . . 46
4.3 Silicon Nitride in the Presence of Oxygen. . . . . . . . . . . . . . . . 47
4.3.1 H¼1 ML Coverage . . . . . . . . . . . . . . . . . . . . . . . . . 49
4
4.3.2 H¼1 ML Coverage . . . . . . . . . . . . . . . . . . . . . . . . . 50
2
4.3.3 H¼3 ML Coverage . . . . . . . . . . . . . . . . . . . . . . . . . 53
4
4.3.4 H = 1 ML Coverage . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.5 Phase Diagram of b-Si N ð1010Þ Surface . . . . . . . . . . 56
3 4
4.3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4 Silicon Nitride in the Presence of Cerium. . . . . . . . . . . . . . . . 60
4.5 Silicon Nitride in the Presence of Oxygen and Rare-Earth
Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5 Atomic-Resolution Study of the Interfacial Bonding at
Si N /CeO Grain Boundaries. . . . . . . . . . . . . . . . . . . . . . . . . . 67
3 4 22d
5.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 Z-contrast Images of Si N /CeO Interfaces . . . . . . . . . . . . . 68
3 4 2–d
5.3 EELS Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6 Atomic-Resolution Study of b-Si N /SiO Interfaces . . . . . . . . . . . 75
3 4 2
6.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.3 Imaging of the Si N /SiO Interface. . . . . . . . . . . . . . . . . . . . 76
3 4 2
6.3.1 Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.4 Thicker Intergranular Films. . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.5 Discussion of the Results and Conclusions . . . . . . . . . . . . . . . 87
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7 Imaging Bulk a-Si N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3 4
7.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.2.1 Imaging a-Si N . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3 4
7.2.2 DFT Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.2.3 EELS Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
8 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100