Baldo and Forrest (Phys. Rev. B 62, 10958, 2000) used transient electrophosphorescence with a phosphorescent sensing layer to measure triplet-exciton transport in amorphous films of tris(8-hydroxyquinoline)aluminum (Alq3), finding a triplet lifetime of τ=25±15\tau=25\pm15 μs, a diffusion coefficient DT=(8±5)×10−8D_T=(8\pm5)\times10^{-8} cm²/s, and a diffusion length of about 140 Å under very high pulsed injection (≈2500 mA/cm²), and reported that the transport is dispersive, i.e., not describable by a single time-independent diffusion coefficient. Their discussion left several issues open. The open problem is a microscopic, experimentally validated account of triplet hopping in neat amorphous Alq3: whether its dispersive transport arises from discrete exciton traps or from the continuous distribution of site energies and hopping rates implied by the film's conformational and meridional/facial isomeric disorder, and how the triplet transport parameters depend on triplet density, reconciling the short high-injection diffusion length with the longer low-current value.

Background

Organic light-emitting devices (OLEDs) are thin films of small organic molecules sandwiched between electrodes; electrically injected electrons and holes recombine into molecular excitons, of which three quarters are spin-forbidden triplet (spin-1) excitons because of spin statistics. Electrophosphorescence harvests these triplets by doping a heavy-metal phosphorescent molecule (a guest, e.g. the platinum porphyrin PtOEP or the iridium complex fac-tris(2-phenylpyridine)iridium, Ir(ppy)3) into an organic host material (e.g. Alq3, the carbazole host CBP (4,4′-bis(N-carbazolyl)-1,1′-biphenyl), or the hole-transport material TPD (N,N′-diphenyl-N,N′-bis(3-methylphenyl)-1,1′-biphenyl-4,4′-diamine)). Triplet excitons migrate between host molecules by Dexter transfer, a short-range electron-exchange mechanism requiring wavefunction overlap, in contrast to the long-range Förster (dipole–dipole) mechanism that dominates singlet transport; the triplet diffusion length LD=DTτL_D=\sqrt{D_T\tau} (with diffusion coefficient DTD_T and lifetime τ\tau) therefore controls whether triplets reach the emitting guest before decaying, and how far they travel. Baldo, O'Brien, You, Shoustikov, Sibley, Thompson and Forrest demonstrated efficient electrophosphorescence from PtOEP in an Alq3 host in 1998, establishing the guest–host phosphorescent OLED architecture. In the source paper, Baldo and Forrest (2000) measured triplet transport in amorphous Alq3 by driving a device with a 200 ns electrical pulse at a current density of roughly 2500 mA/cm² and recording the time-resolved PtOEP phosphorescence from a thin sensing layer separated from the exciton-formation zone by Alq3 spacers of varying thickness, sweeping out residual charge with a reverse bias. Fitting the triplet diffusion equation to these transients yielded τ=25±15\tau=25\pm15 μs, DT=(8±5)×10−8D_T=(8\pm5)\times10^{-8} cm²/s and LD=140±90L_D=140\pm90 Å, but no single constant diffusion coefficient could reproduce both the sharp initial rise and the long tail of the transients: the transport is dispersive, meaning the effective hopping rate decreases as excitons relax deeper into the distribution of localized states, as is well known for charge transport and for triplet transport in low-temperature organic glasses (Richert and Bässler, 1986). The paper attributed the dispersiveness either to exciton traps or to a distribution of diffusion coefficients arising from molecular-conformation variations in the amorphous film, and stated that a detailed microscopic model of triplet hopping in disordered organic hosts was needed; it also noted that the high-injection conditions of the measurement are far above normal OLED operating currents, that the earlier low-current measurement had yielded a longer diffusion length, and enumerated further issues concerning the then-unknown Alq3 triplet energy (no phosphorescence was observable even at 10 K), reverse triplet transfer from Ir(ppy)3 to CBP, the efficiency limit under triplet–triplet annihilation (TTA, the bimolecular loss process in which two triplet excitons annihilate), and the properties of an ideal host. In the standard microscopic picture of disordered molecular films, hopping occurs between sites whose energies form a roughly Gaussian density of states (DOS); if the DOS width is comparable to or larger than the thermal energy kBTk_BT, excitons continuously relax toward lower energies and transport is dispersive, whereas for narrow disorder the system equilibrates and transport becomes non-dispersive (constant DTD_T). This framework, plus the fact that evaporated amorphous Alq3 contains a mixture of meridional and facial molecular isomers with measurably different triplet energies, makes the two hypotheses of the source paper — discrete traps versus continuous energetic/conformational disorder — concrete and testable against the measured transients.

Problem Statement

Determine the microscopic origin of dispersive triplet-exciton transport in neat amorphous Alq3 films, and its dependence on triplet density, as requested by the discussion of Baldo and Forrest (2000): (i) establish whether the dispersiveness observed in the PtOEP-sensing-layer transient measurements — the failure of any single time-independent diffusion coefficient to reproduce both the sharp rise and the long tail of the transients — arises from discrete exciton traps — isolated deep sites, characterized by a trap depth and density, that localize excitons and release them by thermal detrapping — or from a continuous distribution of site energies and Dexter hopping rates, i.e. a single continuous site-energy distribution of width comparable to or larger than k_BT produced by the conformational and meridional/facial isomeric disorder of the amorphous film, by constructing a microscopic model of triplet hopping in disordered Alq3 whose predicted transients reproduce the measured Alq3 transients reported by Baldo and Forrest (2000), and which attributes the dispersiveness to the better-supported of the two mechanisms; and (ii) determine how the Alq3 triplet transport parameters (DTD_T, τ\tau, and the diffusion length LDL_D) depend on the triplet density or injection level over the range from normal OLED operating currents up to the pulsed high-injection conditions (≈2500 mA/cm²) of the original measurement, and determine, once triplet-triplet-annihilation losses are accounted for, which processes account for the reduction of the measured diffusion length relative to the previously reported low-current value.

References

  1. M. A. Baldo and S. R. Forrest, 'Transient analysis of organic electrophosphorescence: I. Transient analysis of triplet energy transfer', Phys. Rev. B 62, 10958 (2000). DOI: 10.1103/PhysRevB.62.10958, https://doi.org/10.1103/PhysRevB.62.10958
  2. M. A. Baldo, D. F. O'Brien, Y. You, A. Shoustikov, S. P. Sibley, M. E. Thompson and S. R. Forrest, 'Highly efficient phosphorescent emission from organic electroluminescent devices', Nature 395, 151 (1998). DOI: 10.1038/25954, https://doi.org/10.1038/25954
  3. M. A. Baldo, C. Adachi and S. R. Forrest, 'Transient analysis of organic electrophosphorescence. II. Transient analysis of triplet-triplet annihilation', Phys. Rev. B 62, 10967 (2000). DOI: 10.1103/PhysRevB.62.10967, https://doi.org/10.1103/PhysRevB.62.10967
  4. R. Richert and H. Bässler, 'Dispersive triplet excitation transport in organic glasses', J. Chem. Phys. 84, 3567 (1986). DOI: 10.1063/1.450243, https://doi.org/10.1063/1.450243
  5. M. Cölle, C. Gärditz and M. Braun, 'The triplet state in tris-(8-hydroxyquinoline)aluminum', J. Appl. Phys. 96, 6133 (2004). DOI: 10.1063/1.1808249, https://doi.org/10.1063/1.1808249
  6. M. Cölle and C. Gärditz, 'Delayed fluorescence and phosphorescence of tris-(8-hydroxyquinoline)aluminum (Alq3) and their temperature dependence', J. Lumin. 110, 200 (2004). DOI: 10.1016/j.jlumin.2004.08.009, https://doi.org/10.1016/j.jlumin.2004.08.009
  7. I. Tanaka, Y. Tabata and S. Tokito, 'Observation of phosphorescence from tris(8-hydroxyquinoline) aluminum thin films using triplet energy transfer from iridium complexes', Phys. Rev. B 71, 205207 (2005). DOI: 10.1103/PhysRevB.71.205207, https://doi.org/10.1103/PhysRevB.71.205207
  8. S. S. R. R. Perumal, B. F. Minaev and H. Ågren, 'Triplet State Phosphorescence in Tris(8-hydroxyquinoline) Aluminum Light Emitting Diode Materials', J. Phys. Chem. C 117, 3446 (2013). DOI: 10.1021/jp309982u, https://doi.org/10.1021/jp309982u
  9. N. C. Giebink, Y. Sun and S. R. Forrest, 'Transient analysis of triplet exciton dynamics in amorphous organic semiconductor thin films', Org. Electron. 7, 375 (2006). DOI: 10.1016/j.orgel.2006.04.007, https://doi.org/10.1016/j.orgel.2006.04.007
  10. S. Watanabe, A. Furube and R. Katoh, 'Generation and Decay Dynamics of Triplet Excitons in Alq3 Thin Films under High-Density Excitation Conditions', J. Phys. Chem. A 110, 10173 (2006). DOI: 10.1021/jp0618227, https://doi.org/10.1021/jp0618227
  11. W. Staroske, M. Pfeiffer, K. Leo and M. J. Hoffmann, 'Single-Step Triplet-Triplet Annihilation: An Intrinsic Limit for the High Brightness Efficiency of Phosphorescent Organic Light Emitting Diodes', Phys. Rev. Lett. 98, 197402 (2007). DOI: 10.1103/PhysRevLett.98.197402, https://doi.org/10.1103/PhysRevLett.98.197402
  12. V. Jankus, C. Winscom and A. P. Monkman, 'Dynamics of triplet migration in films of N,N'-diphenyl-N,N'-bis(1-naphthyl)-1,1'-biphenyl-4,4''-diamine', J. Phys.: Condens. Matter 22, 185802 (2010). DOI: 10.1088/0953-8984/22/18/185802, https://doi.org/10.1088/0953-8984/22/18/185802
  13. O. V. Mikhnenko, R. Ruiter, P. W. M. Blom and M. A. Loi, 'Direct Measurement of the Triplet Exciton Diffusion Length in Organic Semiconductors', Phys. Rev. Lett. 108, 137401 (2012). DOI: 10.1103/PhysRevLett.108.137401, https://doi.org/10.1103/PhysRevLett.108.137401
  14. D. Rai and R. J. Holmes, 'Measurement of the triplet exciton diffusion length in organic semiconductors', J. Mater. Chem. C 7, 5695 (2019). DOI: 10.1039/c9tc00686a, https://doi.org/10.1039/c9tc00686a
  15. M. Ansari-Rad, 'Transport and Annihilation of the Triplets in Organic Phosphorescent Systems: Kinetic Monte Carlo Simulation and Modeling', J. Phys. Chem. C 125, 5760 (2021). DOI: 10.1021/acs.jpcc.0c10138, https://doi.org/10.1021/acs.jpcc.0c10138
  16. W. S. Jeon, T.-J. Park, S. Y. Kim, R. Pode, J. Jang and J. H. Kwon, 'Ideal host and guest system in phosphorescent OLEDs', Org. Electron. 10, 240 (2009). DOI: 10.1016/j.orgel.2008.11.012, https://doi.org/10.1016/j.orgel.2008.11.012
  17. Y. Nagata and C. Lennartz, 'Atomistic simulation on charge mobility of amorphous tris(8-hydroxyquinoline) aluminum (Alq3): Origin of Poole-Frenkel-type behavior', J. Chem. Phys. 129, 084708 (2008). DOI: 10.1063/1.2949506, https://doi.org/10.1063/1.2949506
  18. Y. Luo and H. Aziz, 'Probing triplet-triplet annihilation zone and determining triplet exciton diffusion length by using delayed electroluminescence', J. Appl. Phys. 107, 094510 (2010). DOI: 10.1063/1.3410678, https://doi.org/10.1063/1.3410678