Influence of recombination rates on transient photoluminescence and efficiency of TADF OLEDs

Introduction

An increasing number of companies are adopting the organic light-emitting diodes (OLEDs) technology in their displays because OLEDs achieve a higher contrast ratio and image quality compared to the widespread LCD technology, in addition to being adaptable for curved surfaces.

Unfortunately, OLED displays have a lower luminous efficiency than LCD displays. This means that for a given light spectrum and at the same amount of input power measured in watts, OLEDs output fewer lumens, hence a lower lumen/watt ratio.

Two key figure-of-merits should be introduced to assess the efficiency of light-emitting devices: internal quantum efficiency (IQE) and external quantum efficiency (EQE).

IQE is the amount of diode current (charge carriers injected in the active area) that will produce luminescence (photon emission) from the active region. OLED devices made by thermally-activated delayed fluorescence (TADF) materials as emitters promise an IQE of 100%. TADF molecules can absorb energy to promote electrons from an excited non-emissive state (triplet state, T) to an excited emissive state (singlet state, S). The radiative recombination of excitons in the singlet state causes the luminescence and its intensity depends on the radiative decay rate kf. The reverse intersystem crossing rate (krisc) indicates how efficiently an exciton in the triplet state is transferred to the singlet state, whereas the intersystem crossing rate (kisc) is its opposite. The non-radiative decay rate (knr) indicates the loss rate of the exciton by non-radiative recombination and it is the sum of the non-radiative recombination rate in the singlet state (knrs) and the triplet state (knrt). For high performance, a TADF emissive material must have a high krisc, kf, and low knr to reduce exciton losses. (Figure 1)
You can find a more detailed description of the TADF process in an earlier blog post.

The EQE represents the number of outcoupled photons per injected charge in the OLED. The EQE can be expressed with the following equation:

where ηout is the optical outcoupling efficiency (typically ≈20%), ηcb is the charge balance (probability of electrons and holes to meet and form an exciton), ηS/T is the singlet-triplet factor (fraction of exciton leading to an emissive state) and the PLQY is the photoluminescence quantum yield of the material (noted as ηrad in other texts). The multiplication of ηS/T and PLQY gives the electroluminescence quantum yield (ELQY), which corresponds to the maximum theoretical IQE of the emitting material when ηcb equals 1.

In a previous blog post, we already discussed how to use the simulation software Setfos to optimize the OLED device structure so to boost the EQE by increasing ηout.

Here, we want to present an analysis of the influence of non-radiative recombination rates (knrs and knrt) on the device efficiency as well as how to determine them from experiments. As we will see, the knr rate influences PLQY, and consequently ELQY, hence the negative impact on EQE.
First, to determine the non-radiative decay rates, we need to extract the rates kf, krisc, and kisc by fitting transient photoluminescence (trPL) measurements of TADF films.

Impact of kf, krisc and kisc on luminescence

The rates kf, krisc and kisc modulate the shape of the transient photoluminescence (trPL) decay of a TADF film by controlling the distribution of excitons in the singlet or triplet state. Table 1 shows two systems of ordinary differential equations (ODE), each describing the evolution of the singlets and triplets exciton population depending on the type of excitation. With optical excitation only singlet states are generated, while with electrical excitation both singlets and triplets are generated following spin-statistics, according to which 1/4 of the excitation forms singlets and 3/4 forms triplets. The reference [Haa18] presents a detailed description of the systems of equations.

Table 1: systems of ordinary differential equations describing the evolution of the singlet and triplet exciton populations in the case of optical or electrical excitations.

Using the equations of Table 1 we can now analyze the impact of the rates kf, krisc and kisc on the trPL. For this example, we consider an ideal TADF film without non-radiative recombination rates and sweep each rate from 1E3 (red line) to 1E9 (purple line) s-1 individually. When the rates are not swept, the following values were set: kf=1E7 1/s, kisc=1E7 1/s and krisc=1E6 1/s.

A log-log plot allows visualizing the typical double decay of TADF films, where the first one is the prompt fluorescence occurring immediately after the excitation pulse and the second one, at later times, is the delayed fluorescence resulting from a delayed formation of singlets.

As a general observation, the best TADF film has no delayed fluorescence peak and only a single high intensity peak in the early times. This situation requires the highest krisc and kf possible. In this condition, the excitons move from the triplet to the singlet state at a high frequency and then immediately recombine radiatively.

Extracting the parameters kf, krisc and kisc from trPL fitting

In the following, we will show how to obtain the rates kf, krisc and kisc without considering the non-radiative recombination by fitting an experimental trPL decay with the software Setfos.

We first configure a TADF film with two types of excitons, exciton 1 and exciton 2, which will respectively represent the singlet state and the triplet state. In such a case, the optical generation efficiency is turned on only for exciton 1 and its radiative decay rate corresponds to the rate kf. The transfer rate from exciton 1 to 2 and from exciton 2 to 1 correspond respectively to the rates kisc and krisc. (Figure 3)

Figure 3: schematic illustration of the TADF model without non-radiative recombination rates (left). Setfos tab to configure the exciton properties (right). The colored circles indicate how the exciton states and exciton parameters are named in Setfos.

We do not need to define a specific value for any rate because they will be extracted during the fitting procedure. The exciton rates will be the free parameters that we want the software to vary in order to fit the experimental measurement. (Figure 4)

Since we already have a realistic range of values for the free parameters (see section above), the ideal fitting algorithm is a combination of global plus local optimization algorithms. This entails a first explorative scan (global optimization) in the user-defined range of values for the optimization parameters followed by a finer adjustment (local optimization) of the parameters. You can find more information on the various types of optimization algorithms in the Setfos manual.

Figure 4: free parameters to vary for fitting the target curve.

Lastly, the target is the experimental measurement we want to fit. In this case we input the normalized curve of luminance, which has a decay equivalent to the trPL (Figure 5).

Figure 5: Setfos tab including the target curve to be fitted by varying the free parameters shown in Figure 4.

It is evident from the simulation results in Figure 6 that the global optimization (left figure) is too inaccurate, and it does not provide an acceptable fitting to the experimental data. When both global and local algorithms are considered (right figure), the fitting curve closely follows the experimental one.

Figure 6: fitting result with only global optimization algorithm (left). Fitting result with global and local optimization algorithm (right).

Finally, to confirm the quality of the fitting, we can analyze the mean chi-square value, the correlation matrix, the standard deviation, and the 95% confidence interval outputted by Setfos (Figure 7). For a good quality fit, you should look for: the lowest mean chi-square value, weak correlations in the correlation matrix, small standard deviation, and, a narrow 95% confidence interval. In our case, all these requirements are satisfied and we can conclude that the fitting is of good quality.

Figure 7: Setfos output for the fitting simulation including the values for the mean chi-square value (orange box), the correlation matrix (green box), the standard deviation (blue box) and the 95% confidence interval (purple box) to assess the quality of the fitting.

Now that we know the meaning of kf, krisc and kisc rates, their impact on the trPL and how to extract them from experimental measurements, we will proceed with the study of the influence of the non-radiative decay rates.

Influence of non-radiative decay rate (knr)

Table 2 presents a modified version of the ODE in Table 1 which includes the non-radiative decay rates. Table 2 contains also the formulas for calculating PLQY and ELQY as they are instrumental to evaluate the impact of the non-radiative decay rates on the OLED efficiency.

The reference [Sem22] presents a detailed description of the systems of equations.

Table 2: systems of ordinary differential equations (ODE) describing the evolution of the singlet and triplet exciton populations including the non-radiative recombination rates in the case of optical or electrical excitations and the formulas to calculate PLQY and ELQY.

Considering the systems of equations in Table 2 and that ELQY= ηS/T*PLQY (as shown above), if we assume a certain PLQY measured experimentally, which ELQY should we expect? To reply to this question we must revert the PLQY calculation, ending up with the following equation:

This equation contains two unknowns, knrs and knrt, and therefore a unique solution cannot be found. The equation is anyway solved by imposing different knrt and the respective knrs is calculated. With this approach multiple couples knrs-knrt are found to be solutions of the equation. The other rates (kf, krisc and kisc) can be obtained from the fitting of trPL measurements as shown in the previous section.

In Figure 8 on the x-axis the non-radiative decay goes from completely located in the triplet-state (extreme left) to only singlet-state (extreme right) and four PLQYs (0.6, 0.7, 0.8, and 0.9) are considered. With increasing knrt the ELQY intensity decreases for any PLQY value. Additionally, for a PLQY=0.6 (blue line) the ELQY varies of about 30%, whereas for a PLQY=0.9 (yellow line) the ELQY varies of by only 7%, indicating that a higher PLQY reduces the negative impact of knrt.

Figure 8: for a fixed PLQY of 0.9, 0.8, 0.7, and 0.6 the ELQY is calculated for all possible couples knrs-knrt which are solutions of equation (1). In this calculation the other rates have been supposed known (kf=10E7 s-1, kisc=10E7 s-1 and krisc=10E6 s-1)

The argument above illustrates that it is important to know the non-radiative decay rates of singlet and triplet states separately in order to estimate the final OLED efficiency accurately. A global fitting algorithm that can be used to quantify all excitonic rates at once has been presented by Sem et al. [Sem22] Here we want to briefly present the results.

The full analysis was carried out on emissive films containing the 25ACA and 26ACA TADF molecules at 1wt% and the extracted parameters are shown in Figure 9. The results suggest that kf, kisc, and krisc are all higher in 26ACA and the knrs in 26ACA is almost two orders of magnitude smaller than in 25ACA while knrt is comparable between the two.

The resulting ELQY, or maximum IQE, is 0.36 for 25ACA and 0.69 for 26ACA. The traditional way of calculating the IQE, assuming ηS/T=1, would have predicted values of 0.42 and 0.71 for 25ACA and 26ACA, respectively. It is important to note that in this case the difference between PLQYs and ELQYs is minimal, but as showed in Figure 8 it can be much larger depending on the specific rates considered.

Figure 9: Plot of the decay rates extracted from the fitting algorithm for 25ACA and 26ACA.

The numerical analysis of the 0D ODEs presented here is a simpler alternative to the full electro-optical models in Setfos, where coupled 1D partial differential equations (PDEs) are solved for studying exciton dynamics and their interaction with electrical charges and the optical cavity.

Conclusions

In this work we highlighted the impact of TADF rates on the trPL decay and on the internal and external quantum efficiencies (IQE and EQE) of TADF emitters. Through a system of ordinary differential equations (ODEs) the radiative recombination rate kf, the intersystem crossing rate kisc and its inverse krisc can be extracted from an experimental trPL decay. Their estimation is necessary to calculate the photoluminescence quantum yield (PLQY) and electroluminescence quantum yield (ELQY) and subsequently assess the influence of non-radiative recombination rates (knrt and knrs) on IQE and EQE. We showed that the ELQY can strongly reduce depending on the magnitude of knrs and knrt, demonstrating that the non-radiative recombination should be taken into account when estimating the maximum EQE.

References:

[Sem22] Sem, S. et al. “Determining non-radiative decay rates in TADF compounds using coupled transient and steady state optical data”, J. Mater. Chem. C 2022, 10, 4878-4885.

[Haa18] Haase, N. et al. “Kinetic Modeling of Transient Photoluminescence from Thermally Activated Delayed Fluorescence”, J. Phys. Chem. C 2018, 122, 29173–29179.

Back to the top