Electronic transport properties of copper and gold at atomic scale [Elektronische Ressource] = Elektronische Transporteigenschaften von Kupfer und Gold auf atomarer Skala / vorgelegt von Saeideh Mohammadzadeh

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• Publié par: technische_universitat_chemnitz
• Publié le: 01 janvier 2010
• Nombre de lectures: 21
• Langue: Deutsch
• Poids de l'ouvrage: 7 Mo

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ElectronicTransportPropertiesof
CopperandGoldatAtomicScale
ElektronischeTransporteigenschaftenvon
KupferundGoldaufatomarerSkala
Von der Fakultät für Elektrotechnik und Informationstechnik
der Technischen Universität Chemnitz
genehmigte
Dissertation
zur Erlangung des akademischen Grades
Doktoringenieur(Dr.-Ing.)
vorgelegt
vonM.Sc.SaeidehMohammadzadeh
geboren am 30. Mai 1980 in Marand, Iran
eingereicht am 22. April 2010
Gutachter
Prof.Dr.ThomasGessner
Prof.Dr.IngridMertig
Tag der Verleihung: 23. November 2010To all lovely people in my lifeBibliographische Beschreibung
Electronic Transport Properties of Copper and Gold at Atomic Scale
Mohammadzadeh, Saeideh – 137 S., 53 Abb., 7 Tab., 125 Lit.
Technische Universität Chemnitz,
Fakultät für Elektrotechnik und Informationstechnik
Dissertation (in englischer Sprache), 2010
Referat
In der vorliegenden Arbeit werden die wesentlichen Faktoren, die die elektronischen
Transporteigenschaften von Kontaktstrukturen atomarer Größe aus Kupfer bzw. Gold
bestimmen, theoretisch untersucht. Untersuchungsgegenstand ist eine leitfähige Struk-
tur zwischen zwei kristallinen Elektroden. Um Transportberechungen sowohl unter
Gleichgewichts- als auch unter Nicht-Gleichgewichts-Bedingungen durchführen zu
können, wird die Simulations-Software gDFTB, die auf dem Nicht-Gleichgewichts-
Green-funktionenformalismus in Kombination mit der Dichtefunktional-Tight-Bin-
ding-Methode beruht, eingesetzt. Die elektronischen Eigenschaften der betrachteten
atomaren Drähte werden nur sehr schwach von ihrer kristallinen Orientierung, ih-
rer Länge und der Elektrodenanordnung beeinflusst. Als eektivster geometrischer
Faktor wurde der Leiterquerschnitt gefunden, weil dieser die Anzahl der Leitungs-
kanäle bestimmt. Darüber hinaus werden die erhaltenen Leitfähigkeitsoszillationen
und die linearen Strom-Spannungs-Kennlinien erklärt. Für eine detaillierte Analyse
des Leitungsmechanismus werden bei den Ein-Atom-Kontakten aus Kupfer und Gold
die Übertragungskanäle und ihre Aufspaltung in Atomorbitale betrachtet. Die präsen-
tierten Ergebnisse bieten eine mögliche Erklärung für den Zusammenhang zwischen
Leitfähigkeit und geometrischer Struktur. Die Resultate zeigen eine akzeptable Über-
einstimmung mit den verfügbaren experimentellen und theoretischen Studien.
Stichworte
atomarer Draht; ballistischer Transport; Ein-Atom-Kontakt; elektronische Transport-
eigenschaften; Gold; Kupfer; Leitfähigkeitsoszillationen; lineare Strom-Spannungs-
Beziehung; Nicht-Gleichgewichts-Green-Funktionen Dichtefunktional-Tight-Binding-
Methode; Transmissions-EigenkanäleAbstract
The factors governing electronic transport properties of copper and gold atomic-size
contacts are theoretically examined in the present work. A two-terminal conductor us-
ing crystalline electrodes is adopted. The non-equilibrium Green’s function combined
with the density functional tight-binding method is employed via gDFTB simulation
tool to calculate the transport at both equilibrium and non-equilibrium conditions. The
crystalline orientation, length, and arrangement of electrodes have very weak influence
on the electronic characteristics of the considered atomic wires. The wire width is
found to be the most eective geometric aspect determining the number of conduction
channels. The obtained conductance oscillation and linear current-voltage curves are
interpreted. To analyze the conduction mechanism in detail, the transmission chan-
nels and their decomposition to the atomic orbitals are calculated in copper and gold
single point contacts. The presented results oer a possible explanation for the rela-
tion between conduction and geometric structure. Furthermore, the results are in good
agreement with available experimental and theoretical studies.
Keywords
atomic wire; ballistic transport; conductance oscillation; copper; electronic transport
properties; gold; linear current-voltage characteristic; non-equilibrium Green’s function
density functional tight-binding method; single point contact; transmission eigen-
channelsAcknowledgments
I owe my deepest gratitude to the following people:
Prof. I. Mertig, thesis referee, for the helpful discussion and her ecient com-
ments which have had a remarkable influence on career of the present work.
Prof. T. Gessner, my supervisor, for believing in me and encouraging me, and
for his important support throughout this work.
Dr. R. Streiter, for providing the great opportunity to spend my Ph.D. in
Chemnitz University of Technology, for his great supports, expertise, kindness,
and for all those are not possible to list here.
Dr. A. Pecchia, the author of gDFTB, for the simulation tool, for his patience
with me to answer my crazy questions, for the excellent advices, and for the
welcome in Rome.
Prof. S. E. Schulz and Prof. T. Otto, for their favor and guidance.
Dr. R. Ecke, for her attempts in IRTG plans and for her kindness all the time.
Prof. M. Hietschold, for the fruitful discussion on the conduction mechanism.
Prof. A. Di Carlo, for introducing the calculation method.
Dr. T. Niehaus and Dr. Ch. Kohler¨ , for providing the copper Slater-Koster
parameters and the helpful discussions about DFTB method.
Dr. J. Schuster, for reading the thesis and helpful discussions.
Dipl.-Phys. A. Zienert, for his great helps, fruitful discussions, and his favors.
M.Sc. K. Malekian, for his helps to edit this work and for his kindness, him as
well as Dr. P. Belsky.
Prof. R. Liu, for his supports during the scholar in Fudan University in Shanghai;
and M.Sc. Zh. Zong., for her welcome in China and for her attempts in the joint
paper.
My dear colleagues and friends, S. Rottau, S. Langos, K. Traber¨ , Dr. H. Wolf,
Dr. M. Vogel, A. Messig, Dr. J. Martin, I. Streiter, J. Grunert, R. Lutnyk,
Dr. K. Schulze, Dr. T. Wa¨chtler, J. Hommel, Dr. N. Nemec, and B. Yen, for
their great kindness.
My parents and my sister, for their endless love.
Financial support from the Deutsche Forschungsgemeinschaft within the International
Research Training Group GRK 1215 is gratefully acknowledged.
6List of Commonly Used
Abbreviations and Symbols
Commonly used abbreviations
Abbreviation Meaning
DFTB Density functional tight-binding
GEA Gradient expansion approximation
GGA General gradient
HRTEM High resolution transmission electron microscopy
IETS Inelastic electron tunneling spectroscopy
KKB Keldysh-Kadano-Baym model
LCAO Linear combination of atomic orbitals
LDA Local density approximation
MCBJ Mechanically controllable break junctions
NEGF Non-equilibrium Green’s function method
PL Principle layer
STM Scanning tunneling microscopy
TB Tight-binding model
TEM Transmission electron microscopy
2DEG Two-dimensional electron gas
7ListofCommonlyUsedAbbreviationsandSymbols
Commonly used symbols
Symbol Meaning
n Electronic density deviation
q Deviation of the atomic charge from the neutral atom
" Energy of a free electron
Fermi wavelengthF
Chemical potential of the electrode

Density operator
Conductivity
<
Electrons in-scattering function (lesser self-energy)
>
Holes function
a
Advanced self-energy

r
Retardedgy

Relaxation time
Collision timeel
Phase relaxation time
’
Nuclear part of system wave funtion
Atomic orbitals localized around the atomic centeri
Many-body system wave function
Scattering statesi
Electronic part of system wave function
D Total density operator
D Partial of the contact

e Electron charge
E System eigenvalue
E Exchange and correlation energyXC
f Fermi distribution function of the electrode

iF (r) Spherical s-like radial function00
g(") System density of states
g Green’s function of the Hamiltonian of the contact

G Conductance
G Quantum conductance0
G Green’s function
<
Gs related to the density of occupied states
>G Green’s function to the of empty states
a
G Advanced Green’s function
rG Retardeds
8ListofCommonlyUsedAbbreviationsandSymbols
Symbol Meaning
15h Planck’s constant (4:13566733 10 eV s)
H Time-independent Hamiltonian operator
H Hamiltonian of the contact

H of the device regionD
0H Two-center TB Hamiltonian
I Surface currentS
0J 0 Current flowing from the site n into the site nnn
J Total electron current through the surface SS
k Fermi wave numberF
‘ Elastic mean free pathel
‘ Phase coherence length
’
‘ Localization length

L System dimensions (L ; L ; L )x y z
n(r) Electron density
0n Reference electronic density
R Reflection coecient
R Contact resistancec
T Transmission coecient
T Kohn-Sham kinetic energys
U Classical electrostatic interaction energy (Hartree energy)H
v Kohn-Sham potentiale f f
v Fermi velocityF
V Hamiltonian coupling the device region to the contacts
V Bias voltageb
0V Eective potential corresponding to the reference charge density
9