Challenges in understanding defects in organic materials: a theorist view, focus on conjugated polymers
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1 Challenges in understanding defects in organic materials: a theorist view, focus on conjugated polymers Marília J. Caldas University of São Paulo Scientia Vinces 1
2 Ronaldo Giro Melissa F. Siqueira-Pinto Járlesson G. Amazonas José Maximiano F. Pinheiro Jr Marcelo Alves-Santos Regina Lélis-Sousa Rodrigo Ramos da Silva Arrigo Calzolari, Alice Ruini Layla Martin-Samos, Laura Zoppi, Giovanni Bussi, Andrea Ferretti Elisa Molinari INFM/S3 and University of Modena & Reggio Emilia 2
3 Interest in Organic Conjugated Polymers Optolelectronic devices such as light-emitting devices (OLED) or organic solar cells (OPV): one entire issue this August lightweight (carbon-based), cheap (wet chemistry, self-assembling), flexible (plastic)
4 Interest in Organic Conjugated Polymers Optolelectronic devices such as light-emitting devices (OLED) or organic solar cells (OPV): lightweight (carbon-based), cheap (wet chemistry, self-assembling), flexible (plastic) Need to understand both optical properties: light-matter interaction carrier transport properties: mobilities, phonons, etc.. (sigh) no free lunch: cheap & flexible bound to be dirty and difficult to characterize, difficult to model, difficult to understand, so on & so forth
5 Outline Brief introduction of pertinent polymer properties Theory focus on: ground state only, DFT-based only general morphology & electronic properties morphology of crystalline polymers studies of disordered oligomer films our work on defects in PPV crystals poly-para-phenylene vinylene Conclusions & Perspectives 5
6 Organic Devices OLEDs, OFETs, OPVs: Very nice and revealing figure from Richard Friend s group: whole soup of different disordered materials (figure still lacks the metal electrodes) Indium Tin Oxide Ho et al, Nature 404, 481 (2000) 6
7 Organic Devices OLEDs, OFETs, OPVs: what do we need to know Transport (electrons & holes) along the chain (intra) or inter-chain? Optical properties excitons? excimers? SxT? Interface: abrupt or rough? injection possible? Morphology virtually unkown Effects of morphology? Ho et al, Nature 404, 481 (2000) 7
8 Organic Conjugated Polymers: what we do know PPV disorder in general, but different ways: semi-crystalline grains in amorphous medium
9 Organic Conjugated Polymers: what we do know disorder in general, but different ways: semi-crystalline grains in amorphous medium effect of disorder on transport is not obvious hint from optical properties: Huang et al, Adv. Funct. Mater. 17, 2902 (2007) ITO/MEH-PPV/Al 9
10 Organic Conjugated Polymers: what we do know disorder in general, but different ways: semi-crystalline grains in amorphous medium Gebhart et al, Synth Met 90, 123 (1997) effect of disorder on transport is not obvious hint from optical properties: first guess looking at oligomers: apart from broadening, distinct shift with length 10
11 Organic Conjugated Polymers: what we do know disorder in general, but different ways: semi-crystalline grains in amorphous medium redshift with oligomer length caused by increase in delocalization of π-electrons effect of disorder on transport is not obvious...that can be blocked in a polymer by torsion between rings Mostly wishful-thinking models: migration faster on longer L grain-interfaces the problem conjugation length L DEFECTS: kinks, impurities (anything that goes wrong usually attributed to impurities) 11
12 Organic Conjugated Polymers: what we do know Unhomogeneous plus impurities (wet chemistry...) carrier transport difficult problem Hopping across grains and in-grain transport : which is dominated by impurities? is transport completely dominated by 1D effects? How to model transport? R. A. Street, J. E. Northrup, and A. Salleo, PRB 71, (2005) 12
13 Organic Conjugated Polymers: what we do know Unhomogeneous plus impurities (wet chemistry...) carrier transport difficult problem Hopping across grains and in-grain transport : which is dominated by impurities? focus here: unsubstituted PPV grain crystallites Herring-bone arrangement highly anisotropic, almost one-dimensional in-grain: can transport be completely dominated by 1D effects? 13
14 Organic Conjugated Polymers: what we do not know can theory help for such a complicated problem? Multi-scale Morphology, thousands of atoms Classical Molecular Dynamics Electronic & Optical, up to few hundrends Quantum, fixed geometries either from experiment or from CMD Multi-formalism Classical MD (several different codes and force fields available, parametrization) Semi-empirical Tight-binding MD (also different codes, home made) Density Functional Theory & beyond DFT (very expensive G 0 W 0 home made) Hartree-Fock & beyond HF (small, finite systems) Multi-code DFT: Plane-waves + Diagonalization (ABINIT, espresso) Local basis + Diagonalization (Siesta) Mixed basis + Car-Parrinello (PAW) HF: Local basis (Gaussian) 14
15 Crystalline polymers: recent work simplest that can be: polyethylene (non-conjugated, dense, reasonably well-characterized) Non-bonded interactions critical for morphology: Quantum treatments must incorporate XC in a non-local fairly accurate functional form nm nm W.D.Calllister Jr, Materials science and engineering An introduction John Willey & sons, NY
16 Crystalline polymers: recent work simplest that can be: polyethylene (non-conjugated, dense, reasonably well-characterized) Non-bonded interactions critical for morphology: Quantum treatments must incorporate XC in a non-local fairly accurate functional form vdw-df Dion et al, PRL 92, (2004) DF: revpbe, 400 ev cutoff energy, plane-waves basis set, Ultrasoft pseudopotentials, 4x4x10 Monkhorst-Pack 12 atoms, 20 valence electrons Kleis et al PRB 76, R (2007) Chalmers & Rutgers (D. Langreth) 16
17 Crystalline polymers: recent work simplest that can be: polyethylene (non-conjugated, dense, reasonably well-characterized) Non-bonded interactions critical for morphology: Quantum treatments must incorporate XC in a non-local fairly accurate functional form vdw-df Dion et al, PRL 92, (2004) DF: revpbe, 400 ev cutoff energy, plane-waves basis set, Ultrasoft pseudopotentials, 4x4x10 Monkhorst-Pack 12 atoms, 20 valence electrons Very good agreement (~8%) both LDA & GGA fail miserably Kleis et al PRB 76, R (2007) Chalmers & Rutgers (D. Langreth) 17
18 Crystalline oligomers: recent work Oligomer crystals: reasonably well-characterized Acenes, phenylenes, thiophenes vdw-df Dion et al DF: GGA, 550 ev cutoff energy, plane-wave basis set, ultrasoft pseudopotentials, PWSCF 62 atoms, 170 valence electrons Nabok et al PRB 77, (2008) Leoben (C. Ambrosch-Draxl) 18
19 Crystalline oligomers: recent work Oligomer crystals: reasonably well-characterized Acenes, phenylenes, thiophenes vdw-df Dion et al DF: GGA, 550 ev cutoff energy, plane-wave basis set, ultrasoft pseudopotentials, PWSCF 62 atoms, 170 valence electrons maximum cohesive energies in very good agreement with experiment (where available) Nabok et al PRB 77, (2008) Leoben (C. Ambrosch-Draxl) 19
20 Crystalline PPV: ancient work our focus today, conjugated, reasonably well-characterized Pristine (non-derivatized) herring-bone packing DF only: LDA, 600 ev cutoff energy, plane-wave basis set, norm-conserving pseudopotentials, PWSCF 28 atoms, 76 valence electrons unit cell c, setting angle, bxc angles fixed (a,b) lattice constants, angstroms (5.45; 8.00) experimental values (6.05; 8.07) LDA much too small (GGA does not bind ) need for vdw-df but A. Ferretti, Laurea Thesis, 2001 UNIMORE disordered or defect-containing films??? 20
21 Amorphous-PPV: recent work disordered polymer films difficult to simulate: oligomers Amorphous film: 744 atoms! Yang et al PRB 76, R (2007) Los Alamos NL
22 Amorphous-PPV: recent work Start from Classical Force Fields! disordered polymer films difficult to simulate: oligomers crystal Oligomer crystal: from experiment Amorphous film: MM (reparametrized, fit B3LYP isolated oligomer) condensation through pressure, anneal to get ensemble film Electronic: DFT-PW91, VASP/PAW 744 atoms, 2184 valence electrons superposition isolated oligomers isolated linear oligomer Yang et al PRB 76, R (2007) Los Alamos NL 22
23 Amorphous-PPV: recent work disordered polymer films difficult to simulate: oligomers crystal More linear chains (closer to ideal) would introduce the defects! film in keeping with the conjugation length hypothesis highlights relevance of interchain interaction superposition isolated oligomers isolated linear oligomer Yang et al PRB 76, R (2007) Los Alamos NL 23
24 1D-PPV: brief recollection DFT-LDA, 600 ev cutoff energy, plane-wave basis set, norm-conserving pseudopotentials, PW-SCF* all calculations from now on Conduction Band Minimum Lowest Unoccupied or LUMO-band π-conjugation dominating effect, transport & optical properties Valence Band Maximum Highest Occupied or HOMO-band *espresso code S. Baroni, A. Dal Corso, S. de Gironcoli, and P. Giannozzi,
25 Crystalline 3D-PPV: not so recent single chain 3D herring bone in the crystalline grains, interchain interaction? gap inter-chain interaction Ferretti el al PRL 90, (2003); PRB 69, (2004) UNIMORE&USP GRC-P&LDS
26 Crystalline 3D-PPV: not so recent Effective masses for HB band processes inter-chain interaction very large difference 26
27 Crystalline 3D-PPV: not so recent Intra / Interchain transport : inter-chain interaction activated hopping Transfer integrals again, very large difference: defect-containing crystals? at least for transport, allows for a first approach through 1D single-chain (ballistic-transport), but 27
28 This work, computational approach: the chain is embedded in the crystal: how can we know the chain geometry? we know that torsions and distortions will affect the conjugation length transport! Structure in-bulk Classical molecular mechanics Compass Force Field 3x3x7 (7 monomer units along chain) Electronic structure single-chain 28
29 This work, computational approach: Simple (important) defects coming from environment/preparation (water): H-defects: vacancy H vac and addition H plus O-defect: hydroxyl (OH) Structure in-bulk Classical molecular mechanics Compass Force Field 3x3x7 (7 monomer units along chain) Electronic structure single-chain fixed atomic positions large supercell Plane waves ultrasoft potentials XC PBE espresso code S. Baroni, A. Dal Corso, S. de Gironcoli, and P. Giannozzi,
30 Coherent Electronic Transport (single chain) defect region of polymer chain perfect chain (semi-infinite) Quantum Conductance depends on the local properties of the conductor (transmission - scattering) and the distribution function of the reservoirs Localized Basis Set operators in block matrix form Maximally Localized Wannier functions and WanT code* transmittance from Real-space Green s Function technique* *A. Calzolari, N. Marzari, I. Souza, and M.B. Nardelli, PRB 69, (2004). 30
31 Systems: Hydrogen: H vac H plus 31
32 Hydrogen Defects: levels Vacancy and addition introduce semi-occupied levels at the VBT C1 gap level concentrated on carbon atom Zoppi et al, Phys. Rev. B 78, (2008) GRC-P&LDS
33 Hydrogen Defects: gap states H vacancy: acceptor delocalizes (over just more than two monomers) H addition: acceptor strongly localized conjugation break? Zoppi et al, Phys. Rev. B 78, (2008) 33
34 Hydrogen Defects: transmittance shaded area = transmittance for clean, perfect PPV chain H vacancy is not detrimental to 1D transport, electrons or holes H addition completely blocks 1D transport, electrons or holes Over-coordination of vinylene segment always produces the same blocking of 1D transport 34
35 Systems: Hydroxyl OH: can we trust just a single-chain calculation? 35
36 This work, computational approach: For the hydroxyl defect, we must calculate also the negative (OH - ) charge state later Structure in-bulk neutral Classical molecular mechanics Compass Force Field 3x3x7 (7 monomer units along chain) Electronic structure complete cell fixed atomic positions (~1760 atoms, ~4800 electrons) Plane waves (4 x 10 6!) ultrasoft potentials PBE espresso code S. Baroni, A. Dal Corso, S. de Gironcoli, and P. Giannozzi,
37 Hydroxyl Defect: levels Effect similar to H plus (from here on, Fermi energy at highest occupied level) Defect state in the gap, semi-occupied Complete bulk cell no striking difference with the isolated chain for the neutral state (use later) Calzolari, Ruini & Caldas, to be published 37
38 Hydroxyl Insertion: gap state HOMO-1 highly localized SOMO LUMO 38
39 Hydroxyl Insertion: gap state band-edge states repelled HOMO-1 highly localized SOMO OH - most probable LUMO 39
40 Hydroxyl Insertion: gap state neutral sate, semi-occupied level negatively charged, fully occupied bands strong shift of defect state towards conduction band as we would expect from a highly localized gap state, not really a shallow acceptor (but not a shallow donor either?) E CBM - 0.2eV, full (0/-) DFT results Calzolari, Ruini & Caldas, to be published 40
41 Small list of unresolved questions: Simple details still missing: can we trust gap level positions? Electrical gap only: Many-body effects (including C-X compensation) huge DFT gap (crystalline cell) ~1.25eV Charged calculations in the bulk cell jellium (+ Markov-Payne, negligible=>1/5000 electrons) 128 SP5 processors, ~ PW/proc = PWs 3000 Kohn-Sham states (>4 ev, ~5eV over Fermi) E g =1.37eV still miss sizeable proportion PPV single-chain L. Martin-Samos et al, work in progress 41
42 Small list of unresolved questions: Simple details still missing: can we trust gap level positions? Electrical gap only: Many-body effects (including C-X compensation) huge DFT gap (bulk cell) ~1.25eV HOMO Charged calculations in the bulk cell still miss sizeable proportion can we ever do GW in such a huge cell? Relaxation of charged defects? bulk cell, DF relaxation of selected segment (all those atoms and electrons!) unreliable energies (sigh) can we include vdw-df in such a huge calculation???? slight delocalization 42
43 Conclusions & Perspectives:.. in order to realize higher mobilities, it is necessary to improve crystalline quality and reduce disorder by using polymers that are less prone to structural defects or by employing growth techniques that allow better control over the defects incorporated into the polymer nanocrystals. Chang et al PRB 76, (2007) Carter, Science 321, 800 (2008) Predicting the behavior of molecular, soft, amorphous, or heterogeneous materials poses notable challenges. Interactions in soft materials or molecular crystals are determined in large part by van der Waals forces, which are not described properly by standard XC functionals in DFT. Recent work applying specialized XC functionals (27), GW (28), and periodic local MP2 (5, 29) have the correct physics and show great promise for treating such dispersion forces. With such techniques, properties of materials composed of, e.g., polymers, colloids, and proteins, will be accessible with QM. Caldas, To understand transport properties, we must understand also hopping, and combine onchain vs hopping (statistical, multiscale); To do that, we must have good morphologies, and good electronic structure results; To reach multi-scale modeling, we must be good at QM. 43
44 Conclusions & Perspectives : and I did not even touch on optical properties, excitons, exciton migration, recombination, trapping at defects... note that she mentions explicitly hard materials, conventional semiconductors, strongly correlated materials where are we for organic polymers? we have in this room specialists on every single method quoted in the diagram: Carter, Science 321, 800 (2008) might be another 20 US$ problem? Thank you 44
45 Support INCT/MCT INEO GRC-P&LDS
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