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When the electron is still far from the trapped hole, it will migrate independently from this hole towards the anode. Thus, hole and electron are not bound or correlated. This situation corresponds to the exciton continuum in solid-state semiconductors. However, when the electron migrates into a region given by a specific electron-hole separation R, the positively charged hole will attract the electron. This sepa­ration is reached, when the energy of the Coulomb attraction is of similar size as the larger one of the two values, the mean inhomogeneous distribution of the energy levels of the matrix material or the thermal energy k_BT. Due to the Coulomb attraction, an electron (e) - hole (h) binding results. The binding energy ΔE(e-h) is proportional to 1/(ε·R) and thus depends on the separation R and on the dielectric constant e of the matrix material. Induced by this attraction, the exciton is formed. The Coulomb attraction represents a long-range interaction as compared to nearest neighbor separations.

For the further processes, it is very important to take also the spins of both electron and hole into account. The spin of the hole is given by the spin of the residual electron at the emitter mole­cule. In a quantum mechanical treatment, the two spins can be coupled to four new combined states: One singlet state and one triplet state. The triplet consists of three triplet substates. These substates differ from each other mainly by their relative spin orientations. An energy splitting between the resulting singlet and triplet states may be disregarded at large electron-hole separations. Therefore, the corresponding exciton state is shown in Fig. 1 (middle) just by one energy level. In a statistical limit, all four substates of this exciton state will be formed (populated) with an equal probability. Consequently, one obtains a population ratio of one to three for singlet and triplet substates, respectively.

Driven by electron-hole attraction, the electron will further move on matrix molecules towards the trapped hole. At least, when the electron reaches nearest neighbor matrix molecules of the emitter, an overlap of electron and hole wavefunctions has to be taken into account. The resulting (short-range) exchange interaction leads to an energy splitting of singlet (S) and  triplet (T) states  by ΔE(S-T).  This energy is approximately proportional to exp(-a·R), wherein a is a constant which depends on the respective matrix and the emitter material.

In a final step, the electron jumps in a very fast process directly to the emitter molecule and it results an excited emitter. This process may occur as singlet or triplet path (S-path, T-paths) depending on the initial spin orientation of the electron-hole pair. The corresponding time constants are of the order of one picosecond (see next section). The population of S_m and T_m states, as shown in Fig. 1, is only depicted as an example. Subsequently, the system will exhibit the usual behavior of an optically excited emitter molecule with typical relaxation processes to the lowest excited states and typical emission properties. For detailed discussions of photophysical properties of organometallic triplet emitters it is referred to the Refs. [1, 12a, 12b]. The electronic states of the emitter compound are characterized by the small frame in the diagram of Fig. 1.

Charge transfer states and relaxa­tion paths

The final steps of the mechanisms described above can also be discussed in a slightly diffe­rent way, to illustrate the occurrence of specific singlet and triplet paths. The situation of a lacking electron in the ground state of the doped emitter molecule (dopant D) and of addi­tional electron charge density on nearest neighbor matrix molecules M can be characterized by dopant-to-matrix charge transfer (DMCT) states, specifically by singlet (¹DMCT) and triplet (³DMCT) states.

It may be visualized that these states belong to a large molecular unit that consists of the doped emitter itself and of the first nearest neighbors of matrix molecules. The energy level diagram of this emitter-matrix-cage unit is schematically displayed in Fig. 2. It corresponds to the large frame depicted in Fig. 1. In particular, the states S and T shown in the frame represent the ¹DMCT and ³DMCT states of the large molecular unit. The lower excited states S₀, T₁, S₁ to S_m are largely confined to the doped molecule itself, while the higher lying charge transfer states are spatially more extended to the first matrix coordination sphere. For these latter states, the exchange interaction between the two electrons involved is relatively small. Thus, the energy separation between the ¹DMCT state and the ³DMCT state is expec­ted to be much smaller than singlet-triplet separations of the spatially more confined states of the original dopant itself.

On the basis of the energy level diagram of Fig. 2, one also obtains an information about the relaxation paths from the excited charge transfer states. In particular, the relaxation from the ¹DMCT to lower states will be faster within the system of singlet states than making a spin-flip first. This is due to the fact that spin-orbit coupling in the organic matrix material will be relatively small and thus, intersystem crossing (ISC) is not favored. Consequently, one obtains the fast singlet path that finally populates the S₁ state. (Figs. 1 and 2) Subsequently, the population of the S₁ state will be followed by an ISC to the T₁ state, though usually with a smaller rate. An initial population of the ³DMCT state is similarly followed by a very fast relaxation within the system of triplet states down to the lowest triplet state T₁. (Fig. 2) The beginning of this relaxation process corresponds to the triplet paths in the exciton formation model shown in Fig. 1. The relaxation times within the singlet and triplet system, respectively, are of the order of one picosecond or faster, while the ISC processes can be significantly slower.

Triplet harvesting

Spin-orbit coupling induced by the central metal ion of the emitter complex will not strongly alter the mechanism of exciton formation in an organic matrix material, but it will have drastic effects on the efficiency of electro-luminescence in an OLED device. To illustrate this property, we will compare the efficiency which is obtainable with a purely organic molecule to the efficiency achievable with a transition metal complex, if both molecules exhibit equal photo-luminescence quantum yields. If one assumes that the initial process of exciton formation occurs statistically with respect to the spin orientations, one obtains 25 % of excitons  with  singlet  character and  75 %  with triplet character. At least for small molecules, this view is largely accepted. [2-11]

After exciton formation and relaxations according to the specific singlet and triplet paths, as discussed in the preceeding section, the lowest excited singlet and triplet states are popu­lated. This is valid for organic as well as for organo-transition-metal emitter materials. The corresponding processes are schematically displayed in the middle of Fig. 3. The organic molecule can exhibit an efficient emission as S₁ → S₀ fluorescence, since usually the S₁ → T₁ intersystem crossing rate is small. On the other hand, since the radiative T₁ → S₀ rate is also small, the deactivation of the  T₁ state  occurs  normally  non-radiatively at am­bient temperature. Therefore, 75% of the excitons, the triplet excitons, are lost. Their energy is transferred into heat. (Fig. 3, left hand side.) The conditions are more favorable for transition metal com­plexes, in which the central metal ion carries significant spin-orbit coupling. (Fig. 3, right hand side.) This is particularly valid for transition metal ions of the third row of the periodic table. For these complexes, ISC to the lowest T₁ state is usually very efficient and thus a singlet S₁ emission is not observable. Moreover, the radiative T₁ → S₀ rate can become sufficiently high so that efficient phosphorescence can occur, even at ambient tem­perature. (For a more detailed discussion see Ref. [10].) Consequently, all four possible spin orientations of the excitons can be harvested to populate the lowest T₁ state. In conclusion, by this process of triplet harvesting one can in principle obtain a four times larger electro-luminescence efficiency for triplet emitters than for singlet emitters.  

Exciton formation at matrix molecules versus charge carrier trapping at emitter compounds

Exciton formation and trapping can also occur at matrix sites. Both the lowest singlet and triplet states of matrix molecules will be populated. From there, triplet and singlet exciton diffusion as Frenkel excitons can occur, however, with different transport probabilities. This will alter the spatial distribution of matrix molecules that are excited in singlet and triplet states, respectively, as compared to the situation immediately after excitation. For an efficient OLED, it is mostly requested to harvest the excitation energy completely in an efficiently phosphorescent triplet state of an organometallic dopant. This requires the realization of two distinctly different processes of energy transfer. For example, the singlet excitation energy is transferred by a long-range Förster transfer mechanism from a matrix molecule to the acceptor (dopant). Independently, the triplet excitation energy is also transferred to the acceptor, though by a different process of energy transfer, in particular by the short-range Dexter transfer mechanism. Both transfer mechanisms should be highly efficient and therefore should fulfill the resonance conditions. This can be expressed by non-vanishing spectral overlap integrals of donor emissions and acceptor absorptions. (For background information see, for example [13].) The fulfillment of these two independent conditions for singlet and triplet energy transfer seems to make this concept of material design – apart from specific and selected combinations – less favorable, as compared to systems with charge carrier trapping directly on the triplet emitters, as discussed in Section 2. (Compare also Refs. [10, 14].)font-family: Verdana;

Summary

Organo-transition-metal triplet emitters have a great potential to be applied in OLEDs. Thus, an understanding of the processes, which lead to electron-hole recombination (exciton forma­tion) and to the population of the emissive triplet states is presented. In particular, it is shown that the dynamical process of exciton formation and trapping on an emitter molecule involves charge transfer states which result from excitations of the dopant to its nearest neighbor ma­trix environment. Individual singlet and triplet relaxation paths lead to the population of the lowest excited singlet and triplet states of the dopant. In typical organic molecules with weak spin-orbit coupling and highly forbidden triplet-singlet transitions, triplet state population is transferred into heat (at ambient temperature). Only the singlet state can emit radiatively (fluorescence). On the other hand, in organo-transition-metal compounds, fast inter­system crossing induced by spin-orbit coupling (SOC) effectively depopulates the excited singlet into the lowest triplet state. Again due to SOC, the triplet can decay radiatively as phosphorescence even with high emission quantum yield at ambient temperature. In case of validity of spin statistics only 25% of the excitons can be exploited by organic emitters, while for triplet emitters additional 75% of the excitons are harvested. Thus, the efficiency of light emission in an electro-luminescent device with triplet emitters can be by a factor of four higher than with singlet emitters.

Acknowledgement

Financial support of the Bundesministerium für Bildung und Forschung (BMBF) is acknowledged.

References

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