Charge transport in organic crystals [Elektronische Ressource] / von Frank Ortmann

Sujets

• Physik

Informations

• Publié par: friedrich-schiller-universitat_jena
• Publié le: 01 janvier 2009
• Nombre de lectures: 27
• Langue: Deutsch
• Poids de l'ouvrage: 3 Mo

Extrait

Charge Transport in Organic Crystals
Dissertation
zur Erlangung des akademischen Grades
doctor rerum naturalium (Dr. rer. nat.)
¨Friedrich-Schiller-Universitat Jena
vorgelegt dem Rat der Physikalisch-Astronomischen Fakult¨at
der Friedrich-Schiller-Universit¨at Jena
von Dipl.-Phys. Frank Ortmann
geboren am 08.10.1980 in Mu¨hlhausen/Thu¨ringenGutachter:
1. Prof. Dr. Friedhelm Bechstedt, Friedrich-Schiller-Universit¨at Jena
2. Prof. Dr. Jens Pflaum, Universit¨at Wu¨rzburg
3. Dr. Peter Bobbert, TU Eindhoven, Netherlands
Tag der letzten Rigorosumspru¨fung: 02.07.2009
Tag der ¨offentlichen Verteidigung: 15.07.2009Contents
1 Introduction 1
1.1 Scientific Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 How This Work Contributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Goals of This Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Introduction to Polarons 6
2.1 What is a Polaron? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Polaron Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Description of Polarons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Holstein Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.2 Fr¨ohlich Polarons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Holstein Hamiltonian and Polaron Sizes . . . . . . . . . . . . . . . . . . . . . 11
2.4.1 Large Polarons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.2 Small Polarons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Theory I. Polarons 13
3.1 Derivation of the Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Polaron Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Polaronic Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5 Numerical Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4 Theory II. Charge Transport 23
4.1 Basic Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.1 Kubo Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.2 Polaron Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 25
III CONTENTS
4.1.3 Time Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1.4 Thermal Averages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2 Mobility Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.1 Coherent Band Transport . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.2 Incoherent Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3 Limiting Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3.1 Narrow-Band Approximation . . . . . . . . . . . . . . . . . . . . . . . 36
4.3.2 Low Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3.3 High Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3.4 Small Electron-Phonon Coupling . . . . . . . . . . . . . . . . . . . . . 39
5 Numerical Model Simulations 41
5.1 Comparison of New Approach to Narrow-Band Theory . . . . . . . . . . . . . 41
5.1.1 Coherent Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.1.2 Incoherent Transport. . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.1.3 Total Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2 Mobility Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.3 Variation of Electron-Phonon Coupling Strength . . . . . . . . . . . . . . . . 50
6 Studies of Charge Transport in Crystalline Structures 53
6.1 Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.1.1 Total Energy Calculations and Structural Relaxation . . . . . . . . . . 53
6.1.2 Treatment of Exchange and Correlation . . . . . . . . . . . . . . . . . 54
6.1.3 Vibrational Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.1.4 Electronic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.1.5 Material Parameters for Transport Theory. . . . . . . . . . . . . . . . 56
6.2 Naphthalene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2.2 Charge Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.3 Durene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.3.2 Geometric Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.3.3 Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.3.4 Electronic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67CONTENTS III
6.3.5 Charge Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.4 Guanine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.4.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.4.3 Dynamic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.4.4 Electronic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.4.5 Charge Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
7 Summary and Outlook 88
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Bibliography 92Chapter 1
Introduction
1.1 Scientific Background
Inrecentyears, applicationsbasedonorganicelectronicshavebecomecommonascanbeseen
from displays based upon organic light emitting diodes (OLEDs) [1–3]. Organic semiconduc-
tors have also been used in organic electronic devices such as organic field effect transistors
(OFETs) [4–9], organic thin film transistors (OTFTs) [10, 11], or organic solar cells [12–14].
Besides π-conjugated polymers, in particular organic molecular crystals (OMCs) have at-
tracted strong experimental and theoretical interest since the long-range order in these mate-
rials allows for the study of fundamental questions in physics and chemistry [8, 15–19]. This
includes especially investigations of underlying elementary processes and interactions that
lead to their specific optical and transport properties, which can be markedly different from
those in conventional covalent or ionic crystals such as the traditional semiconductors Si and
GaAs.
The charge transport in OMCs has been under strong debate ever since the pioneering
experimentalworkofKarlet al. [20]whospentdecadespreparingandmeasuringhighquality
organic crystals. Many of these results are still a benchmark today. Karl even succeeded
to demonstrate hot carrier effects in naphthalene crystals. [21] Despite such outstanding
experimental achievements, a recent review article states that the “understanding of charge
transport ... remains limited.” [8]Similarlyanotherrecentreviewexpectsthatcomprehensive
understanding will arise in the future from several improvements in the theoretical modeling
and description of transport. This includes the number of computational studies that has
to be increased but more importantly the required higher level of the theoretical treatment.
[22] The dominating impression from such conclusions in the most recent reviews and books
is that many fundamental questions are not satisfactorily answered.
The natural question arises what is actually understood so far about the charge trans-
12 CHAPTER 1. INTRODUCTION
port in OMCs and why is the situation by far more complex than in traditional inorganic
semiconductors. An excellent indicator of the difficulties in understanding and describing
ˇcharge transport in organic crystals can be found in a monograph by Silinish and C´apek.
[23] They speak of a “mobility puzzle” which is that “on one hand, the mean free path l0
of the carrier ... from room temperature to down to 150 K is actually of the order of lattice
constanta (l ≈a ) and strongly suggests a hopping model approach. On the other hand, the0 0 0
−γtypical (T) dependences ... ∝T are often supposed to speak in favor of some band-type
1carrier transport.” [23] Thereby hopping or band transport in organic crystals are assumed
to be the exclusive transport mechanisms for either localized or delocalized charge carriers,
respectively.
In fact, the bare electronic bandwidth of organic molecular crystals can reach 500 meV
[24–26] or even more [27]. In comparison to the thermal energy this is large and a supporting
argumentforband-liketransportsimilartothecaseofconventionalinorganicsemiconductors.
A large bare bandwidth, however, is not a sufficient criterion for this mode of transport in
organicsemiconductorsandcanonlyserveasanindicatorforhighmobilities. Thisisd