Understanding charge transport in Ir(ppy)₃:CBP OLED films Free

Organic light emitting diodes (OLEDs) emit light by either fluorescence or phosphorescence.^1,2 In traditional fluorescent OLEDs, emission occurs through the radiative decay of singlet excitons. This naturally introduces a limited internal quantum efficiency (IQE) of 25% due to spin probabilities associated with the formation of the excited state.^1,3–5 Alternatively, phosphorescent OLEDs emit light via radiative triplet decay, which is enabled by the presence of heavy atoms such as iridium(iii) or platinum(ii).^1–3,6 Since the triplet state is energetically lower than the singlet state, intersystem crossing can occur spontaneously and is encouraged by the increased spin-orbit coupling associated with heavy metal atoms. Hence, both the singlets and triplets formed in the device can be utilized for light emission.^1,3,7 Indeed, it has been demonstrated that phosphorescent OLEDs can approach an internal quantum efficiency (IQE) of 100%.^1,8–10 However, the most efficient phosphorescent OLEDs usually have the emitter blended with a host to avoid intermolecular interactions that lead to triplet-triplet annihilation.¹¹ 

More recently, thermally activated delayed fluorescence (TADF) OLEDs have also been realized with near 100% IQE by utilizing reverse intersystem crossing, which allows triplet excitons to cross into a radiative singlet state using thermal energy.^3,12,13 A potential advantage of TADF is that it provides a relatively inexpensive alternative to phosphorescent OLEDs by eliminating the requirement of rare metals.¹² However, it remains a challenge to produce high performance TADF-based OLEDs from solution-processable materials,¹² which are of interest for coating large areas for applications such as lighting. Efficient TADF-based OLEDs often also have the emitter blended in a host material at low concentrations (<20 wt. %), although recent work has shown that high efficiency can also be achieved with an emissive layer composed purely of the TADF emitter.¹³ 

In typical guest-host blends that have a low guest concentration, it is generally assumed that the guest is homogeneously distributed throughout the blend.^{7,10,11,14,15} Average guest homogeneity in a blend film has been observed using neutron reflectometry measurements. For example, a blend of fac-tris(2-phenylpyridine)iridium(iii) (Ir(ppy)₃) in 4,4′-bis(N-carbazolyl)biphenyl (CBP) was shown to have an even concentration of the complex in the film normal to the substrate.¹⁶ However, the resolution of the neutron reflectometry experiment is insufficient to conclude that the iridium complexes are fully dispersed and non-interacting in the blend. In fact, it was recently shown using molecular dynamics (MD) simulations that Ir(ppy)₃ guest molecules in a CBP host tend to have a number of neighbors that are metal complexes at concentrations as low as 5 wt. % and provide percolation paths throughout the blend at slightly higher concentrations.¹¹ Understanding how the guest distribution impacts on charge mobility is a key element in optimizing the efficiency of Ir(ppy)₃:CBP OLEDs, as well as other devices that contain guest-host blended active layers.

In this work, the effects of guest concentration on charge transport at steady state are investigated using a Monte Carlo hopping model. In particular, the mobility dependence on guest concentration for an Ir(ppy)₃:CBP blend is explored under the assumption of a random guest distribution. This is then compared to the spatial distribution of charges relative to the guest molecules to gain insight into how the formation of guest clusters and percolative networks counteracts the impact of charge trapping on the guest molecules.

Section II outlines the methods used to generate the morphologies, followed by a description of the transport model. The results are presented in Sec. III, with the summary of the results given in Sec. IV.

Charge transport was simulated using a kinetic Monte Carlo (KMC) model to enable investigation of the relation between transport events and explicit morphology.^17–21 Under the assumption that guest molecules are randomly distributed throughout the host, a cubic lattice morphology was generated by randomly assigning the desired percentage of sites as guest sites. Since each site is assumed to represent one molecule, the percentage of guest sites required to give the desired wt. % was calculated based on the corresponding molar ratio. This calculated percentage was then used as the probability that an individual site is assigned as a guest.

A lattice spacing (a) of 0.8935 nm was implemented to achieve a molecular density similar to the blend film formed by molecular dynamics (MD) deposition and annealing simulations of 6 wt. % Ir(ppy)₃ in CBP. As is common for many organic semiconductor transport models, site energies were chosen from a Gaussian distribution^22–24 with a standard deviation of 162 meV.²⁵ The system structure contained parallel planar electrodes, periodic boundaries in the orthogonal directions, and an overall system size of 71.5 nm × 53.6 nm × 53.6 nm to avoid finite size effects in the periodic directions.²⁶ Sample generated morphologies are shown in Fig. 1.

The KMC model was implemented to utilize a graphics processing unit (GPU) for efficient parallelism.²⁷ At each time step, all possible events of interest were considered, including charge hopping, injection, removal, and recombination. The probability of choosing event i for a given Monte Carlo step was given by

where ν_i is the rate of the event and ν_tot is the sum of all event rates.^18,22,28 The time step was then calculated as

where ξ is a linear random number on the interval (0,1].^17,22,29,30

Charge hopping from site i to site j was modeled using Miller-Abrahams rates, given by²² 

where γ is the inverse localization radius (in this case calculated such that 2γa = 10 is satisfied²²), r_ij is the Euclidean distance between the destination site j and the source site i, k_B is the Boltzmann constant, T is the temperature, $ΔEij=Ej−Ei$ is the difference in energy between a charge on the destination and source sites, and $ν0e(h)$ is the base electron (hole) hopping rate. These hopping rates were calculated for all available hops up to a distance of 3a in each direction to ensure that all probable hopping events are considered.²² The contributions to energy differences included highest occupied/lowest unoccupied molecular orbital (HOMO/LUMO) energy levels (ionization potential/electron affinity), energetic disorder, potential due to the electrodes, and Coulomb interactions between charges and their images, which are detailed further below. An electron hopping to the site of a hole, or vice-versa, was assumed to result in an exciton, which was then removed from the system since exact exciton behavior was beyond the scope of this study. The process of exciton formation was assumed to always be energetically favourable, giving a Boltzmann factor of 1 in Eq. (3).

A full list of system property and simulation values is presented in Table I. The hopping rate values were chosen to give an electron mobility close to 3 × 10⁻⁴ cm²/Vs and a hole mobility close to 2 × 10⁻³ cm²/Vs.³¹ For simplicity, the electron and hole mobilities of Ir(ppy)₃ were assumed to be the same as those of CBP, as was the energetic disorder. The overall site energy distribution of the empty system is therefore a mixed distribution of two Gaussian functions with equal standard deviation (σ) and means equal to the HOMO energy levels of the two materials for holes (or LUMO energy levels for electrons), with the mixing ratio equal to the molar ratio of Ir(ppy)₃ to CBP. The permittivity of CBP was determined from capacitance measurements.

The total electrode and Coulomb potential at each site was calculated by solving Poisson’s equation iteratively to a tolerance of 1 × 10⁻⁷ V for the electrode contribution and 5 × 10⁻⁵ V for the charge contribution. The self-interaction error for charge hopping was suppressed using the “exact” method of Li and Brédas,³³ where the change in Coulomb energy for a hop from site i to site j is adjusted by adding the potential at site j due to a single charge on that site in an otherwise empty system and subtracting the potential at the same site due to a single charge on site i. This required pre-calculating the influence of a charge on each site of an otherwise empty system and storing the results for sites within the hopping range so that they could be rapidly accessed to save processing time. These pre-calculated values were also used as part of an initial estimate of the solution to Poisson’s equation after a hopping or injection event to reduce the number of iterations required for an update. Consequently, the energetic landscape was able to be updated after every Monte Carlo move to maintain accuracy.

The electrodes were made up of a number of sites from which a charge could hop into the system, and injection rates were calculated using the Miller-Abrahams equation.³⁴ The energy penalty for injection was included here in addition to the other energetic considerations of the equation and was calculated as the energy required to separate the charge from its image seen across the electrode.^35,36 The analytical solution to this for a single charge q injected to a perpendicular distance r from an infinite electrode in an otherwise empty system is given by

This becomes more complex with the introduction of periodic boundaries and an opposite electrode due to the increased number of images and is particularly difficult in the presence of dielectric interfaces or electrode structures other than parallel planes. However, it has been shown that in general, the energy to place a charge in a system is equal to half the sum of the energy due to all of its image charges.³⁶ Since the energy for a charge on each site was pre-calculated already as above, these values were also utilized to compute the injection penalty. This method allows for fast computation in a way that is independent of the surrounding system and could therefore be expanded to more complex system structures such as those seen in field effect transistors.

Since the effects of realistic electrode injection were beyond the scope of this study, Ohmic contacts were assumed. This was achieved by treating the Fermi level as being equal to the HOMO energy level of CBP when considering holes and the LUMO energy level when considering electrons and enforcing the condition of zero electric field at the contact. Given that the HOMO and LUMO energy levels of Ir(ppy)₃ are within those of CBP, direct injection into the complex should also be energetically favorable. At regular intervals, the charge on each electrode was calculated based on the total electric field. This was then used to scale the injection rates such that for a planar electrode made up of N interfacial sites with a total charge of Q coulombs, the Miller-Abrahams rate is scaled by a pre-factor of $AQeN$⁠. Here, e is the unit charge and A is a constant to ensure sufficiently high injection rates that will maintain the zero field condition at steady state.

Simulations were performed at various guest concentrations up to 50 wt. % under biases of 5, 7, and 10 V, the range of potentials at which Ir(ppy)₃:CBP OLEDs are known to emit light with increasing luminance.^37,38 At least three different morphology realizations were used for each concentration, and error bars were calculated as the standard deviation between morphologies. To avoid the effects of initial energetic relaxation, all simulation measurements were obtained based on time-averaging at steady state, which was identified through constancy in the charge concentration and device current. Bulk mobilities were then calculated based on average transport properties using the drift-diffusion equation

where J is the current density, E is the electric field, and n is the number density as a function of the direction of travel, x. The field dependence of the mobilities for the various blends was all found to follow a Poole-Frenkel form.³⁹ 

Results from these mobility measurements at various concentrations are shown in Fig. 2, where clear minima can be observed in the vicinity of the blend containing 10 wt. % Ir(ppy)₃. This is most distinct at low voltages, with the curve flattening out significantly under higher bias (i.e., higher fields).

As shown in Fig. 3, the HOMO and LUMO levels of Ir(ppy)₃ are within those of CBP, so the guest molecules act as traps for both electrons and holes. The average portion of time spent by a charge on a guest molecule is illustrated in Fig. 4, which shows that charges are spending a large percentage of their time on the guest molecules, even at low concentrations. It also shows that electrons spend a lower fraction of time on the guest sites compared to holes, which may be due to the smaller difference between the LUMO levels compared to that between the HOMO levels. The results strongly suggest that the view that electron and hole transport and recombination occurs primarily on the host, followed by energy transfer to the guest, is not correct, but rather substantial numbers of charges reside and recombine on the guest.

As the voltage is increased, the trap depth when hopping in the direction of the electric field is effectively reduced, allowing faster escape of charges and reducing the depth of the minima seen in Fig. 2. As indicated by the difference between the electron and hole mobility graphs, a flatter curve is seen for the electrons due to the shallower trapping depth on guest sites. However, a trapping depth that is too small may result in a larger portion of excitons forming on the host molecules, therefore reducing the probability that they diffuse to a guest molecule where they can undergo radiative decay.

In a very low concentration system (<2 wt. %), guest molecules are typically isolated and so each Ir(ppy)₃ molecule can act as a trap, thereby reducing mobility. However, as the concentration increases, the guest molecules can begin to form clusters, providing small pathways along which charges can travel, effectively reducing the overall number of traps in the system compared to the number of guest molecules. A further increase in concentration results in the formation of percolation pathways, which allow charges to travel across significant portions of the device via guest-to-guest hopping. Since the mobility in the guest and host was equal in this system, the minimum mobility at 10 wt. % is therefore reflective of the point at which the maximum number of traps is present.

To understand guest-to-guest hopping, we define a “cluster” as a group of guest molecules that are connected by at most second nearest neighbor hops. This level of connectedness was chosen based on the observation that >99.9% of hops were within a distance of at most the second nearest neighbor. Figure 5 shows an analysis of the number of clusters of guest molecules in comparison with the location of the mobility minima observed in Fig. 2. These results show a striking relationship where the mobility minimum occurs at the same concentration as where the number of clusters is maximized. This suggests that de-trapping from guest clusters is the rate limiting step in the bulk charge transport for guest concentrations used in the highest efficiency OLEDs. It is expected that this mobility minima will shift slightly toward lower guest concentration for a more realistic morphology where clustering is more prevalent.¹¹ 

Although exact exciton dynamics were not studied here, formation events were tracked based on when an electron hopped to a site containing a hole or vice versa. Figure 6 shows the distribution of exciton formation events in relation to their distance to the nearest Ir(ppy)₃ molecule. It can be seen that even at 2 wt. %, a significant portion of singlet and triplet excitons form directly on the guest molecules. Singlet excitons on Ir(ppy)₃ molecules are able to rapidly cross into the triplet state, from which they can radiatively decay due to strong spin-orbit coupling. However, excitons that form on a host molecule must first be transferred to a guest molecule before they can contribute to phosphorescence. Energy transfer from the host to the guest can occur either through Förster or Dexter mechanisms, although Förster transfer between CBP and Ir(ppy)₃ has a relatively low probability due to the small overlap of the CBP emission and Ir(ppy)₃ absorption spectra, and the low optical density of Ir(ppy)₃ at the guest concentrations used.¹¹ Due to the short-range nature of Dexter energy transfer, excitons are likely only able to contribute to phosphorescence if the Ir(ppy)₃ guest is within the exciton diffusion length when the exciton is formed on a host CBP.

It has been experimentally observed that the optimum concentration of Ir(ppy)₃ in CBP for OLEDs is approximately 6 wt. %.³⁷ At this concentration, approximately 60% of the excitons are formed on the guest molecules, with the remainder forming within 3 lattice units (∼2.7 nm), which is sufficiently close to enable Dexter energy transfer from the host to the guest.⁴⁰ These results highlight the importance of charge trapping directly on the guest for high efficiency Ir(ppy)₃:CBP OLEDs. It is likely that these results are applicable to other guest-host systems with similar transport characteristics and concentrations. Given the exponential increase in cluster size shown in Fig. 5, it is apparent that the optimal concentration must be balanced between one that is high enough for any excitons formed on the host to be sufficiently close to guest molecules and that is low enough to minimize triplet-triplet and triplet-charge quenching between connected guest molecules.

While energetic disorder has been shown to have significant effects on organic semiconductor transport,^22,41–46 here only a single value is considered for computational reasons. However, it is expected that an increase in energetic disorder will result in a flatter mobility curve due to the difference in the HOMO (LUMO) levels of the two materials being less significant on the scale of the disorder, indicating less trapping of charges on the guest molecules. Similarly, reduced energetic disorder would lead to the opposite effect, with a more distinct mobility minimum and increased trapping on the guest molecules.

Kinetic Monte Carlo simulations were used to study steady state charge transport in Ir(ppy)₃:CBP OLEDs. Varying the concentration of guest molecules revealed a distinct mobility minimum at approximately 10 wt. % Ir(ppy)₃, which was due to the formation of connected clusters that created effective guest molecule-based trap sites. The depth of the minima was shown to arise from the difference between the host and guest HOMO levels for holes, or LUMO levels for electrons, as well as the electric field. Furthermore, these results indicate that a large portion of excitons are formed directly on the Ir(ppy)₃ molecules, even at low concentrations, with almost 100% of exciton formation events being within 3 lattice units of the nearest guest molecule at a concentration as low as 6 wt. % Ir(ppy)₃. Under the more realistic morphology observed by Tonnelé et al.,¹¹ the mobility minimum is expected to shift slightly towards lower guest concentrations due to the increased clustering of the guest molecules. Future work will aim to utilize a more advanced, off-lattice KMC model using morphologies generated via MD modeling and consider exciton mechanics and additional guest-host blends.

We would like to thank Dr. Thomas Lee and Professor Alan Mark from the University of Queensland for providing access and insight into their molecular dynamics data. We also wish to acknowledge the computational resources provided by the James Cook University High Performance Computing facilities. S.S. was supported by an Australian Government Research Training Program Scholarship. P.L.B. is an Australian Research Council Laureate Fellow (No. FL160100067).