From molecules to mobilities:
modelling charge transport in organic semiconductors
Joseph John Kwiatkowski
Department of Physics, Imperial College London
Submitted in fulfilment of the requirements of the degree of
Doctor of Philosophy
December 2008

To Dziadek, the first to Imperial.

This thesis describes work done between October 2005 and September 2008 in the Experimental Solid State Physics group of Imperial College London, under the supervision of Professor Jenny Nelson. Except in the few places where it is explicitly stated otherwise, the results presented herein are the product of my own work.

Joe Kwiatkowski, December 2008

Acknowledgements
Abstract
Contents
List of Figures
List of Tables
Commonly used symbols and abbreviations
1 Introduction:
Organic semiconductors and charge mobilities
 1.1 Macroelectronics
 1.2 Organic macroelectronics
 1.3 Charge mobilities
 1.4 Understanding charge mobilities in disordered organic semiconductors
 1.5 Modelling charge transport in disordered organic semiconductors
 1.6 Overview and scope of thesis
2 Background 1:
Modelling intermolecular charge transport
 2.1 Delocalised frontier orbitals
 2.2 The mechanism of charge transfer
 2.3 Semi-classical Marcus Theory
 2.4 Quantum chemical calculation of λ, Jif, and ΔE
 2.5 Summary
3 Results 1:
Zero-point vibrations and vibronic coupling
 3.1 Vibronic coupling and charge transfer
 3.2 Quantifying vibronic coupling
 3.3 Results
 3.4 Conclusions
 Acknowledgements:
4 Background 2:
Calculating charge mobilities
 4.1 Calculating charge mobilities
 4.2 The master equation
 4.3 Solving the master equation with kinetic Monte Carlo
 4.4 ToFeT
 4.5 Summary
5 Results 2:
Hole and electron mobilities in tris(8-hydroxyquinoline) aluminum (Alq3)
 5.1 Charge transport in Alq3
 5.2 Methodology
 5.3 Crystalline Alq3: photocurrent transients and mobilities
 5.4 Disordered Alq3: photocurrent transients
 5.5 Disordered Alq3: charge mobilities
 5.6 Conclusions
6 Results 3:
Morphology and mobility in polycrystalline C60 FETs 
 6.1 Modelling C60 FETs
 6.2 Film morphologies
 6.3 Intermolecular charge transfer
 6.4 Simulating FETs
 6.5 Conclusions
 Acknowledgements
7 Conclusion:
From molecules to mobilities
 7.1 Vibronic coupling
 7.2 ToFeT
A Born-Oppenheimer approximation
 A.1 Derivation
B Franck-Condon principle
 B.1 Derivation
C The Bixon-Jortner model
D Quantum Chemistry
 D.1 The molecular electronic Hamiltonian
 D.2 The Hartree-Fock approximation
 D.3 Density Functional Theory
 D.4 Calculating matrix elements between Slater-type wavefunctions
E Qualifying the Franck-Condon approximation in semi-classical Marcus Theory
F Efficiently implementing Kinetic Monte Carlo methods
 F.1 Choosing a wait time
G Probability of total hopping rates for Alq3 and C60
H Software
H. References
In going on with these experiments, how many pretty systems do we build, which we soon find ourselves oblig’d to destroy! If there is no other use discover’d of Electricity, this, however, is something considerable, that it may help to make a vain man humble.

    Benjamin Franklin [10]

Essentially all models are wrong, but some are useful.

    George Box [49]

Ut tensio, sic vis.
(As the extension, so the force.)

    Robert Hooke [65]

Definition of the Monte Carlo technique:
  1. A last resort for numerical integration
  2. A waste of computational time.

    Paraphrase of M. Kalos (a pioneer of the Monte Carlo technique) [81]

Everything flows and nothing abides,
everything gives way and nothing stays fixed.

    Heraclitus

In all chaos there is a cosmos,
in all disorder a secret order.

    Carl Jung [109]

And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.

    T.S. Eliot [134]