Bottom-up modelling of charge transport in organic semiconductors

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1 Bottom-up modelling of charge transport in organic semiconductors David L. Cheung Department of Chemistry & Centre for Scientific Computing University of Warwick LCOPV 2010 Boulder 7th-10th August 2010

2 Acknowledgements People Alessandro Troisi, David McMahon Denis Andrienko (MPI Mainz) Guido Raos (Milan) Sara Fortuna, Dan Jones, Tao Lui, Natalie Martsinovich, Emanuele Maggio, Jack Sleigh (Troisi group) Computers Money Centre for Scientific Computing, University of Warwick EPSRC ERC (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

3 Outline 1 Introduction 2 Charge transport in polymer semiconductors 3 Modelling PCBM 4 Conclusions and outlook (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

Large-area/flexible electronic devices lighting displays

4 Organic semiconductors Organic semiconductors crystalline organics (e.g. pentacene) polymer semiconductors liquid crystals Large-area/flexible electronic devices lighting displays photovoltaics (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

5 Organic semiconductors Compared to inorganic materials, organic electronics have the potential to tailor-make compounds for diverse applications we can make any material we want BUT Relationship between structure and property (charge mobility) not known we don t know what we want to make DLC & A Troisi PCCP 2008 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

6 Organic semiconductors Compared to inorganic materials, organic electronics have the potential to tailor-make compounds for diverse applications we can make any material we want BUT Relationship between structure and property (charge mobility) not known we don t know what we want to make Need to understand charge transport mechanism interplay between electronic & nuclear degrees of freedom disorder (static & dynamic) morphology DLC & A Troisi PCCP 2008 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

Molecular modelling of organic electronics Charge transport is intrinsically quantum solid-state physics/ quantum chemistry Organic materials are soft (classical) molecular

7 Molecular modelling of organic electronics Charge transport is intrinsically quantum solid-state physics/ quantum chemistry Organic materials are soft (classical) molecular simulations Morphology is important coarse-grained simulations Linking across length/ timescales (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

8 Model systems Most investigated organic photovoltaic mixture P3HT PCBM Use combined MD/QC modelling to study mechanism of charge transport in these model systems MD simulations to study microstructure/morphology use representative MD configurations as input to QC calculations (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

9 Outline 1 Introduction 2 Charge transport in polymer semiconductors Microstructure Transport mechanism Connection to phenomenological models 3 Modelling PCBM 4 Conclusions and outlook (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

10 Why study P3HT? Crystalline P3HT forms well-defined lamellar structure high degree of structural order Electronic properties described by models for disordered materials charge transport described by hopping models optical properties: polaron models Where s the disorder? (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

MD simulations Classical MD simulations of crystalline P3HT 12 chains, 40 rings per chain (Mw 6700 Da) Marcon-Raos/OPLS forcefield Anisotropic-NPT MD

11 MD simulations Classical MD simulations of crystalline P3HT 12 chains, 40 rings per chain (Mw 6700 Da) Marcon-Raos/OPLS forcefield Anisotropic-NPT MD simulations Simulation lengths up to 5 ns multiple short simulations (0.3-1 ns) (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

12 Microstructure Dihedral angle distributions System well ordered up to 500 K P(φ 1 ) Ring-ring T=100 K T=300 K Ring-tail type-ii (low-molar mass) polymorph Unremarkable dihedral angle distributions Long range order in the dihedrals Dynamic disorder not important Signs of static disorder P(φ 2 ) φ / degrees φ i / degrees Dihedral angle time series DLC, DP McMahon, & A Troisi JPCB t / ns (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

13 Charge carrier wavefunction Quantum chemical calculations reveal long lived traps HOMO density (from AM1 calculations) at different times t 1 t 2 DLC, DP McMahon, & A Troisi JACS 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

14 Classification of states States classified by... localization time dependence persistent (29%), non-persistent, double (or more) persistent DLC, DP McMahon, & A Troisi JACS 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

15 Where does it trap? Localized traps HOMO localized on planar segments Trap depth > k B T E HOMO E HOMO 1 localized: ± ev non-localized: ± ev DLC, DP McMahon, & A Troisi JACS 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

16 What about polarons? Charge localized by static disorder further localized by electron-phonon coupling In P3HT both deformations are co-operative - molecular planarized by excess charge DLC, DP McMahon, & A Troisi JACS 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

17 Phenomenological models Top-down modelling - device physics 1 Assume transport model (e.g. GDM) number of free parameters, e.g. density of states, transfer integrals 2 Fit parameters to experimental measurements 3 Calculate charge mobility using KMC/Master equation Can estimate key parameters from MD/QC calculations N Tessler et al, Adv Mater 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

18 Density of states Distribution of site energies Edge fit by double Gaussian width of dominant Gaussian 0.1 ev DLC, DP McMahon, & A Troisi JACS 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

19 Transfer integrals Between chains t(r): average transfer integral between rings of separation r t (r) / ev H/H H-1/H H/H-1 H-1/H r / A t generally decreases with distance r / A peak in HOMO-1/HOMO-1, HOMO/HOMO-1, HOMO-1/HOMO transfer integrals at r 5 Å DLC, DP McMahon, & A Troisi JPCB 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

Beyond GDM Non-monotonic behaviour of transfer integrals not seen in models such as GDM Strong coupling between ring separation and orientations p 1 (r) = u 1.u 2 r 1 0.1 0.5 P (r) 0.

20 Beyond GDM Non-monotonic behaviour of transfer integrals not seen in models such as GDM Strong coupling between ring separation and orientations p 1 (r) = u 1.u 2 r P (r) p 1 (r) r / A close approach between S and C-C bond on rings on adjacent chains (overlap of HOMO-1) (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

21 Outline 1 Introduction 2 Charge transport in polymer semiconductors 3 Modelling PCBM Microstructure Electronic states and disorder Localization 4 Conclusions and outlook (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

22 What is PCBM? [6, 6]-phenyl-C 61 -butyric acid methyl ester fullerene derivative organic electron acceptor side chain: solubility, little (direct) effect on charge transport Little studied as a stand-alone material partially disordered, nanocrystalline unknown electronic structure in condensed phase (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

23 MD simulations Simulate 108 PCBM molecules Initial configuration from low temperature (T 90 K) crystal structure orthorhombic crystal 3x3x3 supercell OPLS force field Simulation lengths up to 2.5 ns (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

5 0 15 Fullerene-benzene 10 5 0 4 6 8 10 12 14 16 18 r / A o similar to experimental crystal structure fullerene-fullerene

24 Microstructure & morphology System forms partially ordered, zig-zag layer structure Radial distribution functions 8 Fullerene-fullerene Benzene-benzene 1.5 g(r) Fullerene-benzene r / A o similar to experimental crystal structure fullerene-fullerene separation 10 Å benzene-benzene separation ( 6 Å) larger than in typical organic crystals ( 3.4 Å) DLC & A Troisi JPCC ASAP (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

25 Distribution of overlaps Spatial distribution of overlap between LUMOs 0.01 Histograms of LUMO overlaps between neighbouring molecules 0.03 < S t (r) > P( S t ) r / A o exponential decay with separation independent of T S t log-normal distribution Largest and 2nd largest overlaps per molecule DLC & A Troisi JPCC ASAP (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

26 Density of states LUMO density of states 0.01 DOS(E) E / Hartree three peaks (at LUMO energies for isolated molecules) first peak width approx 0.02 ev DLC & A Troisi JPCC ASAP (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

27 What are the states? Localization characteristics Lα localization length spread (# of molecules containing 90% of density) L α / A o Spread/N E / Hartree E / Hartree Rapid changes in localization behaviour of closely spaced states DLC & A Troisi JPCC ASAP (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

What are the states? E = 0.0505 Hartree E = 0.0503 Hartree E = 0.0486 Hartree E = 0.0450 Hartree E = 0.0432 Hartree E = 0.

28 What are the states? E = Hartree E = Hartree E = Hartree E = Hartree E = Hartree E = Hartree DLC & A Troisi JPCC ASAP (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

29 Why does it localize? Energy difference between molecules (diagonal disorder) distribution of site energies has standard deviation 0.5kB T Electron-phonon coupling ZPE larger than energy difference at transition state Electronic disorder (off-diagonal) DLC & A Troisi JPCC ASAP (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

30 Conclusions Combination of classical and quantum modelling provides a powerful method for the study of the charge transport in soft materials interplay of nuclear and electronic degrees of freedom disorder - dynamic and static Polymer semiconductors combination of MD/QC calculations used to infer charge transport mechanism transfer integrals calculated from MD trajectories show more complex distributions then assumed in charge transport models Organic electron acceptors large differences in localization between different electronic states localization largely due to electronic disorder Further reading D. L. Cheung, D. P. McMahon, and A. Troisi, J Phys Chem, 113, 9393 (2009) D. L. Cheung, D. P. McMahon, and A. Troisi, J Am Chem Soc, 131, (2009) D. L. Cheung and A. Troisi, J Phys Chem C ASAP (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

31 Outlook Bottom-up modelling, from molecular to device scale Classical MD Quantum chemistry Localization DOS Transfer integrals Quantum Dynamics Coarse-grained simulations Device modelling (e.g. Kinetic MC, master equation) (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

32 Outlook Bottom-up modelling, from molecular to device scale Classical MD Quantum chemistry Localization DOS Transfer integrals Quantum Dynamics Coarse-grained simulations Device modelling (e.g. Kinetic MC, master equation) (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

33 Interfaces in OPV Mixtures Interface microstructure and morphology atomistic study of P3HT:PCBM interface (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

34 Outlook Bottom-up modelling, from molecular to device scale Classical MD Quantum chemistry Localization Transfer integrals DOS Quantum Dynamics Coarse-grained simulations Device modelling (e.g. Kinetic MC, master equation) (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

freedom) numerically integrate propogate the wavefunction Calculated charge mobility µ = 2.4 cm 2 V 1 s 1 (c.f. experimental µ 0.

35 Quantum dynamics Conformational disorder in discotic liquid crystal (HBC) timescale of electronic motion timescale of nuclear motion Develop simplified semi-classical model using MD data Langevin dynamics - friction coefficient γ (captures neglected degrees of freedom) numerically integrate propogate the wavefunction Calculated charge mobility µ = 2.4 cm 2 V 1 s 1 (c.f. experimental µ 0.5 cm 2 V 1 s 1 ) A Troisi, DLC, & D Andrienko PRL 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

36 Outlook Bottom-up modelling, from molecular to device scale Classical MD Quantum chemistry Localization DOS Transfer integrals Quantum Dynamics Coarse-grained simulations Device modelling (e.g. Kinetic MC, master equation) (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

Coarse-grain simulations DPD simulations of PATs Phase

Lamellar [A 1 B 1 ] and inverted hexagonal phases [A 2

hexagonal phases [A 1 (B 2 ) 2 ] Relationship between

with experiment DLC & A Troisi PCCP 2009 (University of

37 Coarse-grain simulations DPD simulations of PATs Phase behaviour determined by molecular architecture A m B n Lamellar [A 1 B 1 ] and inverted hexagonal phases [A 2 B 1 ] A m (B n ) 2 Lamellar [A 1 (B 1 ) 2 ] and hexagonal phases [A 1 (B 2 ) 2 ] Relationship between side chain length/density and phase behaviour agrees with experiment DLC & A Troisi PCCP 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

Outlook Bottom-up modelling, from molecular to device scale Classical MD Quantum chemistry Localization DOS Transfer integrals Quantum Dynamics

38 Outlook Bottom-up modelling, from molecular to device scale Classical MD Quantum chemistry Localization DOS Transfer integrals Quantum Dynamics Coarse-grained simulations Device modelling (e.g. Kinetic MC, master equation) (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

39 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

40 Possible transport mechanisms 1 Hopping between localized states (Variable Range Hopping) 2 Distortion drags charge carrier (Conformationally gated transport) 3 Excitation from localized to delocalized state (Mobility edge) (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

41 Top-down modelling Device physics 1 Assume transport model (e.g. GDM) number of free parameters 2 Fit parameters to experimental measurements 3 Calculate charge mobility using KMC/Master equation No clear relationship between molecular structure and model parameters not predictive Instead of imposing a transport model from above, use theory to study systems in microscopic detail and infer charge transport behaviour bottom-up modelling (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

42 Phenomenological theories? Phenomenological theories assume forms for density of states, distribution of transfer integrals... Density of states Transfer integrals 0.2 HOMO/HOMO HOMO-1/HOMO HOMO/HOMO-1 HOMO-1/HOMO t / ev r / A DOS edge approximated by double Gaussian width of dominant Gaussian 0.1 ev Non-monotonic behaviour of t contrary to common assumptions DLC, DP McMahon, & A Troisi JACS 2009; JPCB 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

43 Transfer integrals Distribution of intrachain transfer integrals HOMO/HOMO, HOMO/HOMO-1, HOMO-1/HOMO, HOMO-1/HOMO K (left), 300 K (right) HOMO/HOMO transfer integral very much larger than the others ( 1.10 ev) DLC, DP McMahon, & A Troisi JPCB 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

44 Overlap computation PCBM too large for traditional QC calculations even semi-empirical calculations too expensive approx 75 seconds per pair, 1.4 million pairs Implement reduced QC analysis 1 get standard structure and MOs (ZINDO) for isolated molecule 2 for each pair of molecules superimpose standard structure/mo 3 find atoms in these standard structures within 7.2 Å 4 compute overlap between these atoms (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

45 Interstate coupling Coupling between different states H ij (t) / ǫ i ǫ j For each state i plot the H ij (t) and R ij against ǫ i ǫ j for j with the strongest coupling 6 40 < H ~ ij > / 10-4 Hartree 4 2 R ij / A o ε i -ε j / 10-4 Hartree Strongest coupling typically between states with small energy differences small separations DLC & A Troisi JPCC ASAP ε i -ε j / 10-4 Hartree (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

46 Dynamic and static disorder Localization may occur due to static disorder grain boundaries chamical defects Organic materials bound by soft van der Waals forces disorder induced by thermal motion (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

47 From molecular crystals to polymers Increasing γ leads to transition from dynamic to static disorder DOS independent of γ low γ intermediate γ Time evolution of wavefunction large γ A Troisi & DLC JCP 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

48 Properties of the transition Scaling mobility by temperature T A Troisi & DLC JCP 2009 (University of Warwick) Charge transport in organic semiconductors LCOPV / 46

Charge Extraction from Complex Morphologies in Bulk Heterojunctions. Michael L. Chabinyc Materials Department University of California, Santa Barbara

Charge Extraction from Complex Morphologies in Bulk Heterojunctions Michael L. Chabinyc Materials Department University of California, Santa Barbara OPVs Vs. Inorganic Thin Film Solar Cells Alta Devices