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Nature
Nature
Nature
0028-0836
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7149
10.1038/s41586-024-07149-x
Analysis
A figure of merit for efficiency roll-off in TADF-based organic LEDs
http://orcid.org/0000-0002-6845-1487
Diesing S. 12
http://orcid.org/0000-0002-9701-1923
Zhang L. 12
http://orcid.org/0000-0001-7183-6022
Zysman-Colman E. eli.zysman-colman@st-andrews.ac.uk

2
http://orcid.org/0000-0001-7821-7208
Samuel I. D. W. idws@st-andrews.ac.uk

1
1 https://ror.org/02wn5qz54 grid.11914.3c 0000 0001 0721 1626 Organic Semiconductor Centre, SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews, UK
2 Organic Semiconductor Centre, EaStCHEM, School of Chemistry, St Andrews, UK
27 3 2024
27 3 2024
2024
627 8005 747753
31 3 2023
1 2 2024
© The Author(s) 2024
https://creativecommons.org/licenses/by/4.0/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Organic light-emitting diodes (OLEDs) are a revolutionary light-emitting display technology that has been successfully commercialized in mobile phones and televisions1,2. The injected charges form both singlet and triplet excitons, and for high efficiency it is important to enable triplets as well as singlets to emit light. At present, materials that harvest triplets by thermally activated delayed fluorescence (TADF) are a very active field of research as an alternative to phosphorescent emitters that usually use heavy metal atoms3,4. Although excellent progress has been made, in most TADF OLEDs there is a severe decrease of efficiency as the drive current is increased, known as efficiency roll-off. So far, much of the literature suggests that efficiency roll-off should be reduced by minimizing the energy difference between singlet and triplet excited states (ΔEST) to maximize the rate of conversion of triplets to singlets by means of reverse intersystem crossing (kRISC)5–20. We analyse the efficiency roll-off in a wide range of TADF OLEDs and find that neither of these parameters fully accounts for the reported efficiency roll-off. By considering the dynamic equilibrium between singlets and triplets in TADF materials, we propose a figure of merit for materials design to reduce efficiency roll-off and discuss its correlation with reported data of TADF OLEDs. Our new figure of merit will guide the design and development of TADF materials that can reduce efficiency roll-off. It will help improve the efficiency of TADF OLEDs at realistic display operating conditions and expand the use of TADF materials to applications that require high brightness, such as lighting, augmented reality and lasing.

Efficiency roll-off in a wide range of TADF OLEDs is analysed and a figure of merit proposed for materials design to improve efficiency at high brightness, potentially expanding the range of applications of TADF materials.

Subject terms

Organic LEDs
Organic LEDs
Photonic devices
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Organic light-emitting diodes (OLEDs) are now widely used in displays and are being developed for applications in lighting, sensing and communications1,2. They consist of layers of charge transporting and light-emitting organic semiconductors in between two electrodes, at least one of which is transparent. When the injected charges recombine, they form both singlet and triplet excitons. Spin statistics suggest three triplets form for each singlet, a ratio that has been verified for evaporated OLEDs using low molecular weight emitters21. In OLEDs using fluorescent materials, only the singlets emit light. Phosphorescent OLED materials were therefore developed to obtain light emission from the triplets as well22. These work very well for red and green emission, but there is not yet a blue phosphorescent emitter meeting all commercial requirements23. Consequently, there is currently great interest in thermally activated delayed fluorescence (TADF) as an alternative approach to obtaining light from triplets3,4. Following the pioneering work of Adachi and coworkers in 2011, there have been more than 4,000 papers with the keyword thermally activated delayed fluorescence24,25 (based on results from 16 February 2024 that mention thermally activated delayed fluorescence or TADF since 2011).

A problem in both organic and inorganic LEDs is that as the drive current is increased for more light output, the efficiency decreases26. This is known as efficiency roll-off and is illustrated in Fig. 1a, which shows the efficiency as a function of current density for prototypical examples of fluorescent, phosphorescent and TADF OLEDs3,27,28. Figure 1a shows that the phosphorescent and TADF OLEDs have more than four times the efficiency of the fluorescent OLEDs, but that their efficiency decreases and particularly severely for the TADF OLEDs as the current density is increased. To compare the behaviour of a wide range of OLEDs of each type, we define J90 as the current density at which the external quantum efficiency (EQE) falls to 90% of its peak value, as illustrated in Fig. 1b.Fig. 1 Examples of efficiency roll-off.

a, Efficiency roll-off of prototypical fluorescent (Alq3), phosphorescent (Ir(ppy)2acac) and TADF (4CzIPN) OLEDs3,27,28. b, Schematic graph showing definition of J90. c, Graph of the relation between J90 and EQE1,000 for TADF5,38,39,48–113, fluorescent (Fluo.)28,114–129 and phosphorescent (Phos.)86–88,128–155 devices emitting in the red (R), green (G) and blue (B) regions of the spectrum (for the references, see Methods).

We have extracted J90 from published data on a wide range of OLEDs together with their EQE at a practical luminance of 1,000 cd m−2. These are plotted for each class of OLEDs and each colour in Fig. 1c. The ideal behaviour would be high J90 (for low efficiency roll-off) and high EQE: that is, the top right quadrant of the graph. Most fluorescent OLEDs fall in the green rectangle (A), which is a region of high J90 but low EQE. Most phosphorescent OLEDs (and a few others) fall in the blue rectangle (B). The upper half of this rectangle represents OLEDs with high efficiency and fairly high J90. TADF OLEDs fall mainly in region C. Notably, there is a much wider spread of both EQE and J90 than for the other classes of OLEDs, possibly because TADF OLEDs is a much younger field. The upper right part of region C shows that there are some reports of TADF OLEDs with high EQE and moderately high J90, although lower than for good phosphorescent devices. However, region C also extends to extremely low values of J90 that is, there are many TADF devices experiencing significant efficiency roll-off at current densities below 0.1 mA cm−2. Even for a green device, this would correspond to a brightness of at most 100 cd m−2, whereas typical displays run at 400 cd m−2 and their individual pixels often run at much higher brightness to achieve an average 400 cd m−2 on the display29. Hence, many reported TADF OLEDs have severe efficiency roll-off and even the best have significant efficiency roll-off (J90 of a few mA cm−2).

Efficiency roll-off in TADF devices

This brings us to the central question of this analysis, which is, what can be done in terms of emitter design to reduce efficiency roll-off (that is, increase J90)? In other words, which photophysical processes need to be tuned by molecular design to minimize inherent limitations of the emitter that contribute to efficiency roll-off? Efficiency roll-off arises both from the emitter design and the device design, but for an optimized device design (for example, balanced charge carriers and wide recombination zone) it will ultimately be limited by the properties of the emitter.

To identify the crucial parameters for emitter design, we first need to consider what causes efficiency roll-off. Studies in phosphorescent OLEDs have shown that triplet–triplet annihilation (TTA) and triplet–polaron annihilation (TPA) are the main loss mechanisms as the current density is increased29–31. A similar understanding is developing in TADF OLEDs in which TTA, TPA and singlet–triplet annihilation (STA) may all contribute32–34. These are all bimolecular processes and thus much more severe at higher excitation densities. Furthermore, as all these processes involve triplets, they can be mitigated by reducing the triplet lifetime and hence reducing the triplet population. This has been achieved successfully in phosphorescent OLEDs by engineering the light-emitting material (for example, by using an iridium complex) to show a large radiative rate constant from the triplet state and thus achieving a relatively short triplet lifetime of around 1 µs. For comparison, delayed fluorescence lifetimes in organic TADF materials range from 1 µs to beyond 500 μs. We briefly note that as well as reducing efficiency, bimolecular processes involving triplets are also a main mechanism of device degradation, providing a further reason to reduce the triplet population in operating devices35.

Hence to reduce efficiency roll-off, we need to reduce triplet lifetime or, more precisely, the triplet population during device operation. This, however, is not as simply achieved as in the case of phosphorescence. The key photophysical processes in a TADF emitter are shown in Fig. 2. Singlets are converted to triplets via intersystem crossing (ISC) with rate constant kISC, and triplets to singlets via reverse intersystem crossing (RISC) at rate constant kRISC. There is potentially radiative and non-radiative decay of both triplets and singlets, although in a good TADF material krS will be much larger than any of knrS, krT and knrT (refs. 36,37). The main approach advocated in the literature for reducing efficiency roll-off is to increase kRISC, commonly by reducing the energy difference between singlet and triplet excited states (∆EST) through molecular design by reducing the exchange integral between the highest occupied and lowest unoccupied molecular orbitals. In addition, there have been other attempts to increase kRISC, for example by the use of heavy atoms, to increase spin–orbit coupling (SOC)5,38. The emphasis on kRISC is so strong that since 2016 there have been 16 publications in the Nature family alone exploring kRISC (refs. 5–20). However, the expected improvement in J90 has not always materialized.Fig. 2 Simplified Jablonski diagram of a TADF emitter.

The excited singlet and triplet states S1 and T1, respectively, are shown in equilibrium due to the occurrence of both intersystem crossing (kISC) and reverse intersystem crossing (kRISC) enabled by the small energy gap (ΔEST) between S1 and T1. A TADF OLED emits light by radiative decay from S1(krS), whereas non-radiative decay from both S1(knrS) and T1(knrT), as well as the negligible radiative decay from T1(krT) are other deactivation pathways of excited species.

To understand how J90 depends on kRISC, we have plotted the graph shown in Fig. 3. There is some correlation (Spearman correlation ρ = 0.638) in so far as there is a tendency towards higher J90 for higher kRISC, but there is an enormous spread of the data (considering this is a log–log plot). For example, the blue dashed rectangle shows that J90 of roughly 2 mA cm−2 can be achieved with kRISC from 2 to 20 × 105 s−1. The insufficiency of kRISC as a guide for molecular design is vividly demonstrated by the red dashed rectangle that shows J90 for molecules designed with a high kRISC of 8–15 × 105 s−1. The values of J90 range from 0.03 to 40 mA cm−2, that is, by more than three orders of magnitude, showing kRISC alone is inadequate as a predictor of efficiency roll-off.Fig. 3 Data analysis.

J90 of the reported TADF OLEDs with respect to kRISC (Spearman correlation ρ = 0.638). Red crosses present TADF molecules containing heavy atoms that benefit from enhanced SOC to increase kRISC. Data inside the dashed boxes are for comparison.

Derivation of FOM

To develop guidelines for TADF materials design to reduce efficiency roll-off in OLEDs, we should first look more closely at Fig. 2 and the mechanism of TADF.

The physics of TADF is often studied using transient photoluminescence (PL) measurements in which the emitter is excited using a laser pulse. Excitons are generated in the excited singlet state (S1), and the decay of the excited state is slowed by cycling to and from the triplet state (T1) by ISC and RISC, respectively. In an OLED, charge injection leads to a buildup of both S1 (25%) and T1 (75%) excitons as well as polarons. There is a dynamic equilibrium between S1 and T1 facilitated by the ISC/RISC cycling. To ascertain on which side the dynamic equilibrium lies, an equilibrium constant Keq is defined as1 Keq=S1T1.

For a three-level TADF OLED under low constant current electrical excitation, the equilibrium constant is given as follows (see Methods for the derivation)2 Keq=3kRISC+kT3kS+kISC,

where kS is the sum of the rate constants for ISC (kISC), radiative (krS) and non-radiative (knrS) decay from S1, and kT is the sum of the rate constants for RISC (kRISC), radiative (krT) and non-radiative (knrT) decay from T1. As explained earlier, to minimize the EQE roll-off a low T1 population is necessary to suppress TTA and to a lesser extent STA and TPA. For an OLED operated at high brightness this translates to the requirement of maximizing the S1 population relative to the T1 population, which can be achieved by maximizing Keq. Furthermore, according to Le Chatelier’s principle, an equilibrium can be moved to a desired product by removing the product from the equilibrium. Here, the radiative decay of S1 excitons is the desired product. Therefore, to minimize the fraction of triplet excitons in the steady-state OLED emitters should be developed (or selected) to maximize the product of radiative rate constant and equilibrium constant. In a good OLED, nearly all electrically excited excitons decay radiatively, that is knrS=knrT=0. Thus, for a TADF emitter with photoluminescence quantum yield near unity and no phosphorescence contribution (krT=0), which is reasonable for good organic emitters, a figure of merit (FOM) for efficiency roll-off can be formulated as3 krSKeq=4krSkRISC3krS+4kISC.

Figure 4 shows J90 plotted as a function of this FOM. There is a stronger correlation with J90 (ρ = 0.700) than kRISC with J90 (ρ = 0.638). Higher krSKeq leads to higher J90. Accordingly, maximizing krSKeq and thus minimizing the T1 population under electrical excitation is a better strategy for improving efficiency roll-off than considering kRISC alone. Figure 4 compares efficiency roll-off as a function of our FOM (black circles) with efficiency roll-off as a function of kRISC (small grey circles). The FOM has a narrower spread of values as would be expected for the improved correlation.Fig. 4 FOM.

Correlations between J90 and krSKeq with a Spearman correlation coefficient of ρ = 0.700. Red crosses identify TADF molecules containing heavy atoms that enhance SOC, which leads to an increase in kRISC. In grey circles, the correlation of J90 and kRISC from Fig. 3 is shown for comparison.

It is interesting to apply this FOM to recent attempts to increase kRISC by incorporating heavy atoms into the molecule to increase SOC5,38. These studies are shown by red crosses in Figs. 3 and 4. This strategy is broadly successful at leading to fast kRISC but does not necessarily lead to the highest J90 as kISC also increases, or krS decreases. This interplay between these parameters is captured by the FOM as can be seen from the red crosses in Fig. 4 being in the same region as other materials. At the same time, incorporation of these larger atoms that result in weaker bonds also leads to faster non-radiative pathways and potentially poor device stability. Here, we can see that kRISC and the proposed FOM give distinct assessments of the heavy atom approach, and that the latter is a better predictor of J90 for future molecular design. Another possible guide for design is (as for phosphorescent devices) short delayed fluorescence lifetime (τDF)39. The correlation of J90 with τDF is shown in Extended Data Fig. 1a. There is a good correlation (ρ = −0.685), although still some scatter. Actually, τDF has a much stronger correlation with the proposed FOM (ρ = −0.801) than with kRISC (ρ = −0.709). In other words, the proposed FOM not only predicts the efficiency roll-off, but also clarifies the key physical processes that need to be optimized to achieve low efficiency roll-off. Although measuring τDF would be an effective way of screening materials for low potential efficiency roll-off after they have been synthesized, our FOM gives more insight into how to design a material for low efficiency roll-off by showing the exact combination of rate constants that should be optimized.

For many TADF materials kISC is substantially faster than krS, in which case the FOM can be simplified to4 krSKeq≈krSkRISCkISCforkrT=knrT=knrS=0andkISC≫krS

This simplified FOM highlights the competition between kISC, kRISC and krS very clearly. It is equivalent to krSKeq in the regime where krS is smaller than kISC (Extended Data Fig. 2).

Other factors affecting efficiency roll-off

Although there is a good correlation between J90 and the proposed FOM, there is a significant spread of data points in Fig. 4. This can be understood to arise because efficiency roll-off involves a combination of the intrinsic properties of the emitting molecule with the extrinsic properties of the device. An analogous situation exists when using photoluminescence quantum yield as a predictor of device efficiency: whether a material realizes its full potential also depends on the device. Similarly, our FOM describes the best that could be achieved with a particular light-emitting material in a device limited by the triplet population. In real devices, many factors, especially imperfect charge balance, could lead to worse performance than this ideal case, and hence can explain the spread of the data in Fig. 4. In addition, at low current density some devices show efficiency increasing with current density, as can be seen for the devices in Fig. 1a. As J90 is taken as a reduction from peak efficiency, this will lead to higher values of J90 than in devices with peak efficiency at very low current. There is another example of this effect in Extended Data Fig. 3 that compares two 2CzPN devices3,40. It should also be noted that practice for determining rate constants varies37,41, which could also contribute to the spread.

Another important factor that could contribute to the spread of data is that the effect of a given triplet population depends on the material. In particular, reported TTA rate constants γTT are widely spread over eight orders of magnitude (10−18–10−10 cm3 s−1)32,33,42,43. So, increasing the FOM will reduce triplet population, and is beneficial (increases J90) but the improvement arising from the reduced triplet population depends on the value of γTT. Similar considerations apply to STA, in which again there is a range of γST, and the relative importance of STA and TTA depends on the relative values of γTT and γST. As these rate constants are not yet widely measured, we have not at this stage attempted to incorporate them into a FOM. However, we show their potential effect in Extended Data Fig. 4, which shows calculations of how J90 would depend on FOM for systems with krS between 105 and 1010 s−1, kISC/krS between 10−1 and 103, and krSKeq between 102 and 108 s−1 for a range of values of γST, γTT and krS. Extended Data Fig. 3a shows how for a given FOM, each order of magnitude change in γTT leads to an order of magnitude change in J90. Extended Data Fig. 4b shows the potential interplay between TTA and STA. The J90 value behaves nearly linearly with krSKeq when only TTA is considered (red dots, the slope is 2). If only STA is considered, there is still a correlation; however, at the same FOM, higher J90 is achieved when krS is large. If both TTA and STA are significant, then the efficiency is limited by TTA at low FOM and by krS at high FOM.

We also note that the kinetics of thin films can result in a multi-exponential transient PL, which is caused by conformational disorder44. Such a decay can be analysed using a Laplace transformation of the three-level kinetics of each conformer45. Our analysis does not include conformational disorder but could be applied in a similar manner to the analysis of multi-exponential transient PL caused by conformational disorder.

Conclusion

Our analysis has important implications for the rapidly growing field of TADF OLED development. At present, many such devices suffer such severe efficiency roll-off that they are unsuitable for practical application and, as we have shown, current emitter design focusing on maximizing kRISC alone is not an effective strategy. On the basis of the insight from considering the quasi-equilibrium in TADF, we instead propose that the focus of materials design and development should shift to maximizing a FOM that combines the physical processes that determine efficiency roll-off. Target values of the FOM will depend on the requirements of particular applications, as well as device design and severity of bimolecular effects. We estimate values of FOM required for materials with chromaticity close to the BT2020 standard46, and with Gaussian emission spectra of width 15 nm in the blue, 30 nm in the green and 45 nm in the red. We use the calculation for Extended Data Fig. 4a with γTT = 10−13 cm3 s−1 and find the FOM required to achieve 90% of a peak EQE of 25% at a brightness of 1,000 cd m−2. We find that for a deep blue emitter (λmax = 467 nm, CIE 1931 colour space (0.131, 0.049)) a FOM of at least 1.5 × 105 s−1 is required. For a green emitter (λmax = 529 nm, CIE (0.169, 0.772)) a FOM of 5.1 × 104 s−1 would be required, and for red (λmax = 650 nm, CIE (0.708, 0.292)) an FOM of at least 1.3 × 105 s−1 is needed.

In terms of material design for low efficiency roll-off, it is not necessary to maximize kRISC, but it is very desirable to maximize kRISC relative to kISC (without sacrificing krS). It is also a useful strategy to seek materials with high krS (providing kRISC/kISC is not reduced), which is also the underlying physics for hyperfluorescent OLEDs47, where the rate constant of Förster resonance energy transfer takes the place of krS in the FOM and lowers the triplet population on the TADF sensitizer. At the same time, there is a need to understand which process dominates the efficiency roll-off. Whereas all main annihilation processes scale with the triplet population and thus inversely with our proposed FOM, the relative importance of these processes in each OLED is not sufficiently known. Therefore, there is a need to measure both γST and γTT in a wider set of devices to fully understand how the excited-state kinetics of the emitter need to be engineered to reduce efficiency roll-off.

We hope that our FOM and these insights will enable the field of TADF OLEDs to overcome the challenge of efficiency roll-off and advance more rapidly to applications in displays, lighting and beyond.

Methods

Data collection

We considered the reported efficiency roll-off behaviour of TADF OLEDs published in peer-reviewed journals between 2016 and 2022. The data of the OLED and emitter were included in the analysis if the following criteria were met:The reported OLED was vacuum-processed, in a bottom-emitting device structure with a TADF emitter in a host material.

Photophysical characterization of the thin film used as the emission layer was reported.

The photoluminescence quantum of the emitter film was reported to exceed 60%.

The calculation of all TADF rate constants was clearly detailed.

Device data clearly showed J90 data or the presented device data allowed for a reasonable estimation of J90.

Applying these criteria led to a total of 66 devices from 46 publications being included in our analysis5,38,39,48–84,156–160.

For comparison, Fig. 1c shows the relation between J90 and the EQE at 1,000 cd m−2 (EQE1,000) for TADF OLEDs5,38,39,48–113 with representative fluorescent28,114–129 and phosphorescent86–88,128–155 devices across red, green and blue colours.

Steady-state population of the excited states

The kinetics of a TADF emitter as shown in Fig. 2 under electrical excitation can be described by the rate equations for the excited singlet state (S1) and the triplet state (T1) when neglecting annihilation processes as follows.5 ddt[S1]t=−(krS+knrS+kISC)⏟=ks[S1]t+kRISC[T1]t+14γ[n]t2

6 ddt[T1]t=−(krT+knrT+kRISC)⏟=kT[T1]t+kISC[S1]t+34γ[n]t2

where kS is the sum of the rate constants for ISC (kISC), radiative (krS) and non-radiative (knrS) decay from S1, where kT is the sum of the rate constants for RISC (kRISC), radiative (krT) and non-radiative (knrT) decay from T1, and γ is the Langevin recombination rate. The derivative of the polaron population [n]t can be sufficiently approximated by not distinguishing between the charge of the polaron as7 ddt[n]t=J(t)ed−γ[n]t2,

where J(t) is the current density at time t, d is the thickness of the emission zone and e is the elementary charge.

In normal device operation, the OLED is driven at constant current density (J(t) = Jconst) so the excited-state populations reach a steady state given by equation (8).8 [n]=Jconstγed.

The steady-state population of S1 and T1 ([S1] and [T1], respectively) can be obtained by substituting the differential equation for S1 in steady state into the differential equation of T1 steady state9 ddt[S1]=−kS[S1]+kRISC[T1]+14γ[n]2=0

10 ⇒[S1]=kRISC[T1]+14γ[n]2kS

11 ddt[T1]=−kT[T1]+kISC[S1]+34γ[n]2=0

12 ⇒[T1]=kISCkRISC[T1]+14γ[n]2kS+34γ[n]2kT=kISCkRISCkSkT[T1]+kISCkS+3γ[n]24kT

13 ⇔[T1]=kISCkS+3γ[n]24kT1−kISCkRISCkSkT=kISC+3kS4(kTkS−kISCkRISC)γ[n]2=3krS+3knrS+4kISC4kS(krT+knrT)+4kRISC(krS+knrS)γ[n]2

14 ⇒[S1]=1kSkRISC[T1]+14γ[n]2=kRISCkISC+3kS(kTkS−kISCkRISC)+1γ[n]24kS=kRISCkISC+3kSkS(krT+knrT)+kRISC(krS+knrS)+1γ[n]24kS

By inserting equation (8) in equations (13) and (14) the steady-state populations are given as a function of the current density as15 S1=kRISC3krS+3knrS+4kISCkSkrT+knrT+kRISCkrS+knrS+114kSJconsted

16 T1=3krS+3knrS+4kISC4kSkrT+knrT+4kRISCkrS+knrSJconsted

Calculation of J90 for OLED examples

A set of 1,287 kinetic parameters for the equations (5) and (6) was generated, using the permutation of the input variables in Extended Data Table 1, with17 kRISC=krSKeq34+kISCkrS

and a thickness of the emission zone of d = 10 nm, a Langevin recombination rate161 of γ=6.8×10−17m3s as well as all other rate constants set to 0.

For the calculation of Extended Data Fig. 3a,b, the bimolecular rate constants were set to the values shown in the figure. J90 was obtained by minimizing equation (18) using the python package scipy162.18 (η¯EQE−0.9)2=ηEQE(J)ηEQE0−0.92=ηIQE(J)ηIQE0−0.92

where ηIQE(J) is the internal quantum efficiency (IQE) at current density J considering annihilation processes and ηIQE0 is the IQE without considering annihilation processes. Both are given by19 ηIQE=(krS[S1]+krT[T1])γdJ

For ηIQE0, the singlet population [S1] and triplet population [T1] were obtained from equations (15) and (16), respectively.

For ηIQE(J), [S1] and [T1] were obtained by minimizing the set of differential equations (20) and (21) with [n] given by equation (7), using the python package scipy161,162.20 ddt[S1]=−(krS+knrS+kISC)⏟=kS[S1]+kRISC[T1]+14γTT[T1]2−γST[T1][S1]+14γ[n]2

21 ddt[T1]=−(krT+knrT+kRISC)⏟=kT[T1]+kISC[S1]−54γTT[T1]2+34γ[n]2

Calculation of target value

The optical power flux Φ leaving an OLED relates to the current density J as22 Φe=∫Φe(λ)dλ=∫hcλI(λ)ηEQEJedλ=hceηEQEJ∫1λI(λ)dλ

where I(λ) is the relative intensity of the OLED at wavelength λ, ηEQE is the ratio of photons leaving the OLED to the number of electrons flowing around the electrical circuit (EQE).

The total luminous flux ΦV can be calculated from the optical power flux using the photonic sensitivity curve V(λ) as23 ΦV=Km∫Φe(λ)V(λ)dλ=KmhceηEQEJ∫1λI(λ)V(λ)dλ

where Km = 683 lm W−1 is a fudge factor called the peak response.

Under the assumption of Lambertian emission, the luminance LV of the OLED is then given as follows.24 LV=ΦVπ=KmhcπeηEQEJ∫1λI(λ)V(λ)dλ

Therefore, the current density required to generate a given luminance by an OLED with a given normalized spectrum and given EQE is given as follows.25 J=1KmπehcLVηEQE∫1λI(λ)V(λ)dλ−1

For the calculation of the target value, we have taken three assumed spectra for red, green and blue with a Gaussian shape and a full-width at half-maximum of 45, 30 and 15 nm, respectively. The centre wavelength was selected so that the colours of the three spectra are as close as possible to the primary colours of the BT.2020 standard in the CIE 1931 colour space, which are given by the coordinates (0.708, 0.292), (0.170,0.797) and (0.131,0.046), respectively46.

The calculation was performed at an EQE of 22.5% for Lv = 1,000 cd m−2, indicating a maximum EQE of 25%. The correlation for J90 to the FOM is taken from the simulated relationship shown in Extended Data Fig. 4a for γTT = 10−13 cm3 s−1 and γST = γTP = 0 as follows.26 logJ901Am−2=2logkrSKeq1s−1−8.3764

27 ⇔krSKeq=10logJ901Am−2+8.37642s−1

Online content

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Supplementary information

Peer Review File

Extended data figures and tables

Extended Data Fig. 1 Correlation with delayed fluorescence lifetime τDF.

(a) Dependence of J90 on τDF with a Spearman correlation, ρ, of  −0.685. (b) Dependence of τDF on kRISC (ρ = −0.709). (c) Dependence of τDF on krSKeq (ρ = −0.801). Red crosses identify TADF molecules containing heavy atoms that enhance SOC, which leads to an increase in kRISC.

Extended Data Fig. 2 Simplified Figure of Merit.

(a) Correlation between J90 and the simplified FOM of krSkRISC/kISC with a Spearman correlation of ρ = 0.680, showing a better correlation than kRISC but a less precise predictor than the FOM of krSKeq. Red crosses identify TADF molecules containing heavy atoms that enhance SOC, which leads to an increase in kRISC. In grey circles, the correlation of J90 and kRISC from Fig. 3 is displayed for comparison. (b) Deviation between the FOM of krSKeq and its simplification of krSkRISC/kISC for kRISC = 107 s–1 showing a deviation between the FOMs for systems with competitive krS and kISC.

Extended Data Fig. 3 Device influence on Roll-off.

Comparison of efficiency roll-off of two literature 2CzPN OLEDs showing different J90 because of different efficiency rise at low current densities3,40.

Extended Data Fig. 4 Impact of STA and TTA on roll-off.

The impact of STA and TTA on the correlation between J90 and krSKeq calculated for a simplified three-level system with krS between 105 s–1 and 1010 s–1, kISC/krS between 10–1 and 103 and krSKeq between 102 s–1 and 108 s–1 (a) for three different TTA rate constants and (b) for a particular STA rate, a particular TTA rate and a particular combination of STA and TTA rate.

Extended Data Table 1 Parameters for Extended Data Fig. 4

Parameters for Extended Data Fig. 4

Generating parameters for the tested set of theoretical emitters shown in Extended Data Fig. 4.

Extended data

is available for this paper at 10.1038/s41586-024-07149-x.

Supplementary information

The online version contains supplementary material available at 10.1038/s41586-024-07149-x.

Acknowledgements

We are grateful to the Engineering and Physical Sciences Research Council of the UK for financial support through grant nos. EP/R035164/1 and EP/P010482/1. We are grateful to K. Yoshida for discussions relating to the target values for the FOM.

Author contributions

I.D.W.S. proposed an FOM approach to efficiency roll-off and wrote the first draft of the paper. L.Z. performed the data acquisition. S.D. provided the derivation. L.Z., S.D. and I.D.W.S. performed the analysis. All authors reviewed and edited the manuscript.

Peer review

Peer review information

Nature thanks Hironori Kaji, Xian-Kai Chen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Data availability

The data supporting this publication can be accessed at 10.17630/d1439596-7eef-44ae-90cd-667b70588896.

Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

These authors contributed equally: S. Diesing, L. Zhang, I. D. W. Samuel
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References

1. Forrest SR The path to ubiquitous and low-cost organic electronic appliances on plastic Nature 2004 428 911 918 10.1038/nature02498 15118718
2. Hong G A brief history of OLEDs-emitter development and industry milestones Adv. Mater. 2021 33 e2005630 10.1002/adma.202005630 33458866
3. Uoyama H Goushi K Shizu K Nomura H Adachi C Highly efficient organic light-emitting diodes from delayed fluorescence Nature 2012 492 234 10.1038/nature11687 23235877
4. Wong MY Zysman-Colman E Purely organic thermally activated delayed fluorescence materials for organic light-emitting diodes Adv. Mater. 2017 29 1605444 10.1002/adma.201605444
5. Hu YX Efficient selenium-integrated TADF OLEDs with reduced roll-off Nat. Photonics 2022 16 803 810 10.1038/s41566-022-01083-y
6. Cui L-S Fast spin-flip enables efficient and stable organic electroluminescence from charge-transfer states Nat. Photonics 2020 14 636 642 10.1038/s41566-020-0668-z
7. Wada Y Nakagawa H Matsumoto S Wakisaka Y Kaji H Organic light emitters exhibiting very fast reverse intersystem crossing Nat. Photonics 2020 14 643 649 10.1038/s41566-020-0667-0
8. Luo Y Ultra-fast triplet-triplet-annihilation-mediated high-lying reverse intersystem crossing triggered by participation of nπ*-featured excited states Nat. Commun. 2022 13 6892 10.1038/s41467-022-34573-2 36371489
9. Gillett AJ Dielectric control of reverse intersystem crossing in thermally activated delayed fluorescence emitters Nat. Mater. 2022 21 1150 1157 10.1038/s41563-022-01321-2 35927434
10. Aizawa N Harabuchi Y Maeda S Pu YJ Kinetic prediction of reverse intersystem crossing in organic donor-acceptor molecules Nat. Commun. 2020 11 3909 10.1038/s41467-020-17777-2 32764588
11. Zysman-Colman E Molecular designs offer fast exciton conversion Nat. Photonics 2020 14 593 594 10.1038/s41566-020-0696-8
12. Yu Y Mallick S Wang M Börjesson K Barrier-free reverse-intersystem crossing in organic molecules by strong light-matter coupling Nat. Commun. 2021 12 3255 10.1038/s41467-021-23481-6 34059685
13. Stranius K Hertzog M Borjesson K Selective manipulation of electronically excited states through strong light-matter interactions Nat. Commun. 2018 9 2273 10.1038/s41467-018-04736-1 29891958
14. Etherington MK Gibson J Higginbotham HF Penfold TJ Monkman AP Revealing the spin–vibronic coupling mechanism of thermally activated delayed fluorescence Nat. Commun. 2016 7 13680 10.1038/ncomms13680 27901046
15. Schleper AL Hot exciplexes in U-shaped TADF molecules with emission from locally excited states Nat. Commun. 2021 12 6179 10.1038/s41467-021-26439-w 34702836
16. Li F Singlet and triplet to doublet energy transfer: improving organic light-emitting diodes with radicals Nat. Commun. 2022 13 2744 10.1038/s41467-022-29759-7 35585063
17. Wu X The role of host–guest interactions in organic emitters employing MR-TADF Nat. Photonics 2021 15 780 786 10.1038/s41566-021-00870-3
18. Gillett AJ Spontaneous exciton dissociation enables spin state interconversion in delayed fluorescence organic semiconductors Nat. Commun. 2021 12 6640 10.1038/s41467-021-26689-8 34789719
19. Fan X-C Ultrapure green organic light-emitting diodes based on highly distorted fused π-conjugated molecular design Nat. Photonics 2023 17 280 285 10.1038/s41566-022-01106-8
20. Zhao W He Z Tang BZ Room-temperature phosphorescence from organic aggregates Nat. Rev. Mater. 2020 5 869 885 10.1038/s41578-020-0223-z
21. Segal M Baldo MA Holmes RJ Forrest SR Soos ZG Excitonic singlet-triplet ratios in molecular and polymeric organic materials Phys. Rev. B 2003 68 075211 10.1103/PhysRevB.68.075211
22. Baldo MA Highly efficient phosphorescent emission from organic electroluminescent devices Nature 1998 395 151 154 10.1038/25954
23. Cai X Su S-J Marching toward highly efficient, pure-blue, and stable thermally activated delayed fluorescent organic light-emitting diodes Adv. Funct. Mater. 2018 28 1802558 10.1002/adfm.201802558
24. Endo A Efficient up-conversion of triplet excitons into a singlet state and its application for organic light emitting diodes Appl. Phys. Lett. 2011 98 083302 10.1063/1.3558906
25. Citation Report (Web of Science, accessed 16 February, 2024); www.webofscience.com/wos/woscc/citation-report/ad524515-2457-4194-9799-2409c8bd955f-cc8165d0.
26. Murawski C Leo K Gather MC Efficiency roll-off in organic light-emitting diodes Adv. Mater. 2013 25 6801 6827 10.1002/adma.201301603 24019178
27. Chiu C-H A phosphorescent OLED with an efficiency roll-off lower than 1% at 10 000 cd m−2 achieved by reducing the carrier mobility of the donors in an exciplex co-host system J. Mater. Chem. C 2022 10 4955 4964 10.1039/D1TC04473G
28. Giebink NC Forrest SR Quantum efficiency roll-off at high brightness in fluorescent and phosphorescent organic light emitting diodes Phys. Rev. B 2008 77 235215 10.1103/PhysRevB.77.235215
29. Huang Y Hsiang EL Deng MY Wu ST Mini-LED, Micro-LED and OLED displays: present status and future perspectives Light: Sci. Appl. 2020 9 105 10.1038/s41377-020-0341-9 32577221
30. Ligthart A Effect of triplet confinement on triplet-triplet annihilation in organic phosphorescent host-guest systems Adv. Funct. Mater. 2018 28 1804618 10.1002/adfm.201804618
31. Coehoorn R van Eersel H Bobbert PA Janssen RAJ Kinetic Monte Carlo study of the sensitivity of OLED efficiency and lifetime to materials parameters Adv. Funct. Mater. 2015 25 2024 2037 10.1002/adfm.201402532
32. Masui K Nakanotani H Adachi C Analysis of exciton annihilation in high-efficiency sky-blue organic light-emitting diodes with thermally activated delayed fluorescence Org. Electron. 2013 14 2721 2726 10.1016/j.orgel.2013.07.010
33. Hasan M Probing polaron-induced exciton quenching in TADF based organic light-emitting diodes Nat. Commun. 2022 13 254 10.1038/s41467-021-27739-x 35017481
34. Thakur K Zee B Wetzelaer GJAH Ramanan C Blom PWM Quantifying exciton annihilation effects in thermally activated delayed fluorescence materials Adv. Opt. Mater. 2021 10 2101784 10.1002/adom.202101784
35. Scholz S Kondakov D Lussem B Leo K Degradation mechanisms and reactions in organic light-emitting devices Chem. Rev. 2015 115 8449 8503 10.1021/cr400704v 26230864
36. Dias FB Penfold TJ Monkman AP Photophysics of thermally activated delayed fluorescence molecules Methods. Appl. Fluoresc. 2017 5 012001 10.1088/2050-6120/aa537e 28276340
37. Tsuchiya Y Exact solution of kinetic analysis for thermally activated delayed fluorescence materials J. Phys. Chem. A 2021 125 8074 8089 10.1021/acs.jpca.1c04056 34473511
38. Matsuo K Yasuda T Blue thermally activated delayed fluorescence emitters incorporating acridan analogues with heavy group 14 elements for high-efficiency doped and non-doped OLEDs Chem. Sci. 2019 10 10687 10697 10.1039/C9SC04492B 32206251
39. Kim JU Nanosecond-time-scale delayed fluorescence molecule for deep-blue OLEDs with small efficiency rolloff Nat. Commun. 2020 11 1765 10.1038/s41467-020-15558-5 32286281
40. Wong MY Deep-blue oxadiazole-containing thermally activated delayed fluorescence emitters for organic light-emitting diodes ACS Appl. Mater. Interfaces 2018 10 33360 33372 10.1021/acsami.8b11136 30192504
41. Serevičius T TADF parameters in the solid state: an easy way to draw wrong conclusions J. Phys. Chem. A 2021 125 1637 1641 10.1021/acs.jpca.0c10391 33576226
42. Niwa A Triplet-triplet annihilation in a thermally activated delayed fluorescence emitter lightly doped in a host Appl. Phys. Lett. 2018 113 083301 10.1063/1.5025870
43. Rossi D Palazzo D Di Carlo A Auf der Maur M Drift‐diffusion study of the IQE roll‐off in blue thermally activated delayed fluorescence OLEDs Adv. Electron. Mater. 2020 6 2000245 10.1002/aelm.202000245
44. Serevičius T Emission wavelength dependence on the rISC rate in TADF compounds with large conformational disorder Chem. Commun. 2019 55 1975 1978 10.1039/C8CC08906J
45. Kelly D Franca LG Stavrou K Danos A Monkman AP Laplace transform fitting as a tool to uncover distributions of reverse intersystem crossing rates in TADF systems J. Phys. Chem. Lett. 2022 13 6981 6986 10.1021/acs.jpclett.2c01864 35881847
46. BT.2020: Parameter Values for Ultra-High Definition Television Systems for Production and International Programme Exchange. ITN www.itu.int/rec/R-REC-BT.2020-2-201510-I/en (2015).
47. Nakanotani H High-efficiency organic light-emitting diodes with fluorescent emitters Nat. Commun. 2014 5 5016 10.1038/ncomms5016 25247589
48. Duan C Multi-dipolar chromophores featuring phosphine oxide as joint acceptor: a new strategy toward high-efficiency blue thermally activated delayed fluorescence dyes Chem. Mat. 2016 28 5667 5679 10.1021/acs.chemmater.6b01691
49. Yang T Improving the efficiency of red thermally activated delayed fluorescence organic light‐emitting diode by rational isomer engineering Adv. Funct. Mater. 2020 30 2002681 10.1002/adfm.202002681
50. Park IS Lee J Yasuda T High-performance blue organic light-emitting diodes with 20% external electroluminescence quantum efficiency based on pyrimidine-containing thermally activated delayed fluorescence emitters J. Mater. Chem. C 2016 4 7911 7916 10.1039/C6TC02027E
51. Zhang D Cai M Zhang Y Zhang D Duan L Sterically shielded blue thermally activated delayed fluorescence emitters with improved efficiency and stability Mater. Horiz. 2016 3 145 151 10.1039/C5MH00258C
52. Lee J Aizawa N Yasuda T Isobenzofuranone- and chromone-based blue delayed fluorescence emitters with low efficiency roll-off in organic light-emitting diodes Chem. Mat. 2017 29 8012 8020 10.1021/acs.chemmater.7b03371
53. Miwa T Blue organic light-emitting diodes realizing external quantum efficiency over 25% using thermally activated delayed fluorescence emitters Sci. Rep. 2017 7 284 10.1038/s41598-017-00368-5 28325941
54. Park IS Komiyama H Yasuda T Pyrimidine-based twisted donor-acceptor delayed fluorescence molecules: a new universal platform for highly efficient blue electroluminescence Chem. Sci. 2017 8 953 960 10.1039/C6SC03793C 28451232
55. Rajamalli P New molecular design concurrently providing superior pure blue, thermally activated delayed fluorescence and optical out-coupling efficiencies J. Am. Chem. Soc. 2017 139 10948 10951 10.1021/jacs.7b03848 28745874
56. Chen JX Red organic light-emitting diode with external quantum efficiency beyond 20% based on a novel thermally activated delayed fluorescence emitter Adv. Sci. 2018 5 1800436 10.1002/advs.201800436
57. Furue R Highly efficient red-orange delayed fluorescence emitters based on strong π-accepting dibenzophenazine and dibenzoquinoxaline cores: toward a rational pure-red OLED design Adv. Opt. Mater. 2018 6 1701147 10.1002/adom.201701147
58. Zhang D Song X Cai M Kaji H Duan L Versatile indolocarbazole-isomer derivatives as highly emissive emitters and ideal hosts for thermally activated delayed fluorescent OLEDs with alleviated efficiency roll-off Adv. Mater. 2018 30 1705406 10.1002/adma.201705406
59. Ahn DH Highly twisted donor-acceptor boron emitter and high triplet host material for highly efficient blue thermally activated delayed fluorescent device ACS Appl. Mater. Interfaces 2019 11 14909 14916 10.1021/acsami.9b00931 30924634
60. Braveenth R High efficiency green TADF emitters of acridine donor and triazine acceptor D–A–D structures J. Mater. Chem. C 2019 7 7672 7680 10.1039/C9TC02491C
61. Chen JX Red/near-infrared thermally activated delayed fluorescence OLEDs with near 100% internal quantum efficiency Angew. Chem. Int. Ed. 2019 58 14660 14665 10.1002/anie.201906575
62. Cheng Z Achieving efficient blue delayed electrofluorescence by shielding acceptors with carbazole units ACS Appl. Mater. Interfaces 2019 11 28096 28105 10.1021/acsami.9b07820 31290328
63. Xie FM Rational molecular design of dibenzo[a,c]phenazine-based thermally activated delayed fluorescence emitters for orange-red OLEDs with EQE up to 22.0 ACS Appl. Mater. Interfaces 2019 11 26144 26151 10.1021/acsami.9b06401 31298023
64. Xie FM Efficient orange–red delayed fluorescence organic light‐emitting diodes with external quantum efficiency over 26% Adv. Electron. Mater. 2019 6 1900843 10.1002/aelm.201900843
65. Balijapalli U Utilization of multi-heterodonors in thermally activated delayed fluorescence molecules and their high performance bluish-green organic light-emitting diodes ACS Appl. Mater. Interfaces 2020 12 9498 9506 10.1021/acsami.9b20020 32020791
66. Kumar A Doubly boron-doped TADF emitters decorated with ortho-donor groups for highly efficient green to red OLEDs Chem. Eur. J. 2020 26 16793 16801 10.1002/chem.202002968 32779254
67. Lim H Highly efficient deep-blue OLEDs using a TADF emitter with a narrow emission spectrum and high horizontal emitting dipole ratio Adv. Mater. 2020 32 e2004083 10.1002/adma.202004083 33079442
68. Peng CC Highly efficient thermally activated delayed fluorescence via an unconjugated donor-acceptor system realizing EQE of over 30 Adv. Mater. 2020 32 e2003885 10.1002/adma.202003885 33118645
69. Yoon J Asymmetric host molecule bearing pyridine core for highly efficient blue thermally activated delayed fluorescence OLEDs Chem. Eur. J. 2020 26 16383 16391 10.1002/chem.202002655 32686232
70. Balijapalli U Tetrabenzo[a,c]phenazine backbone for highly efficient orange-red thermally activated delayed fluorescence with completely horizontal molecular orientation Angew. Chem. Int. Ed. 2021 60 19364 19373 10.1002/anie.202106570
71. Chan C-Y Stable pure-blue hyperfluorescence organic light-emitting diodes with high-efficiency and narrow emission Nat. Photonics 2021 15 203 207 10.1038/s41566-020-00745-z
72. Chen JX Managing locally excited and charge-transfer triplet states to facilitate up-conversion in red TADF emitters that are available for both vacuum- and solution-processes Angew. Chem. Int. Ed. 2021 60 2478 2484 10.1002/anie.202012070
73. Chen Y Approaching nearly 40% external quantum efficiency in organic light emitting diodes utilizing a green thermally activated delayed fluorescence emitter with an extended linear donor-acceptor-donor structure Adv. Mater. 2021 33 e2103293 10.1002/adma.202103293 34516019
74. Duan C Manipulating charge‐transfer excitons by exciplex matrix: toward thermally activated delayed fluorescence diodes with power efficiency beyond 110 lm W−1 Adv. Funct. Mater. 2021 31 2102739 10.1002/adfm.202102739
75. Karthik D Acceptor-donor-acceptor-type orange-red thermally activated delayed fluorescence materials realizing external quantum efficiency over 30% with low efficiency roll-off Adv. Mater. 2021 33 e2007724 10.1002/adma.202007724 33792077
76. Kim H Lee Y Lee H Hong JI Lee D Click-to-twist strategy to build blue-to-green emitters: bulky triazoles for electronically tunable and thermally activated delayed fluorescence ACS Appl. Mater. Interfaces 2021 13 12286 12295 10.1021/acsami.1c00278 33661594
77. Nagata M Fused-nonacyclic multi-resonance delayed fluorescence emitter based on ladder-thiaborin exhibiting narrowband sky-blue emission with accelerated reverse intersystem crossing Angew. Chem. Int. Ed. 2021 60 20280 20285 10.1002/anie.202108283
78. Tanaka H Hypsochromic shift of multiple-resonance-induced thermally activated delayed fluorescence by oxygen atom incorporation Angew. Chem. Int. Ed. 2021 60 17910 17914 10.1002/anie.202105032
79. Chen JX Optimizing intermolecular interactions and energy level alignments of red TADF emitters for high-performance organic light-emitting diodes Small 2022 18 e2201548 10.1002/smll.202201548 35491513
80. Gao H Ultrapure blue thermally activated delayed fluorescence (TADF) emitters based on rigid sulfur/oxygen-bridged triarylboron acceptor: MR TADF and D-A TADF J. Phys. Chem. Lett. 2022 13 7561 7567 10.1021/acs.jpclett.2c01745 35948077
81. Mahmoudi M Ornamenting of blue thermally activated delayed fluorescence emitters by anchor groups for the minimization of solid-state solvation and conformation disorder corollaries in non-doped and doped organic light-emitting diodes ACS Appl. Mater. Interfaces 2022 14 40158 40172 10.1021/acsami.2c12475 36000983
82. Mamada M Highly efficient deep‐blue organic light‐emitting diodes based on rational molecular design and device engineering Adv. Funct. Mater. 2022 32 2204352 10.1002/adfm.202204352
83. Masimukku N Bipolar 1,8-naphthalimides showing high electron mobility and red AIE-active TADF for OLED applications Phys. Chem. Chem. Phys. 2022 24 5070 5082 10.1039/D1CP05942D 35146498
84. Zhang HY A novel orange-red thermally activated delayed fluorescence emitter with high molecular rigidity and planarity realizing 32.5% external quantum efficiency in organic light-emitting diodes Mater. Horiz. 2022 9 2425 2432 10.1039/D2MH00639A 35839078
85. Xia G A TADF emitter featuring linearly arranged spiro-donor and spiro-acceptor groups: efficient nondoped and doped deep-blue OLEDs with CIE(y) <0.1 Angew. Chem. Int. Ed. 2021 60 9598 9603 10.1002/anie.202100423
86. Song W [1,2,4]Triazolo[1,5-a]pyridine-based host materials for green phosphorescent anddelayed-fluorescence OLEDs with low efficiency roll-off ACS Appl. Mater. Interfaces 2018 10 24689 24698 10.1021/acsami.8b07462 29974742
87. Li W Li J Liu D Wang F Zhang S Bipolar host materials for high-efficiency blue phosphorescent and delayed-fluorescence OLEDs J. Mater. Chem. C 2015 3 12529 12538 10.1039/C5TC02997J
88. Zhang Z Excited-state engineering of universal ambipolar hosts for highly efficient blue phosphorescence and thermally activated delayed fluorescence organic light-emitting diodes Chem. Eng. J. 2020 382 122485 10.1016/j.cej.2019.122485
89. Ni F Teaching an old acceptor new tricks: rationally employing 2,1,3-benzothiadiazole as input to design a highly efficient red thermally activated delayed fluorescence emitter J. Mater. Chem. C 2017 5 1363 1368 10.1039/C7TC00025A
90. Zhang YL High-efficiency red organic light-emitting diodes with external quantum efficiency close to 30% based on a novel thermally activated delayed fluorescence emitter Adv. Mater. 2019 31 e1902368 10.1002/adma.201902368 31490581
91. Gong X A red thermally activated delayed fluorescence emitter simultaneously having high photoluminescence quantum efficiency and preferentially horizontal emitting dipole orientation Adv. Funct. Mater. 2020 30 1908839 10.1002/adfm.201908839
92. Wang YY Positive impact of chromophore flexibility on the efficiency of red thermally activated delayed fluorescence materials Mater. Horiz. 2021 8 1297 1303 10.1039/D1MH00028D 34821922
93. Kim BS Lee JY Engineering of mixed host for high external quantum efficiency above 25% in green thermally activated delayed fluorescence device Adv. Funct. Mater. 2014 24 3970 3977 10.1002/adfm.201303730
94. Sun JW A fluorescent organic light-emitting diode with 30% external quantum efficiency Adv. Mater. 2014 26 5684 5688 10.1002/adma.201401407 24890507
95. Seino Y Inomata S Sasabe H Pu YJ Kido J High-performance green OLEDs using thermally activated delayed fluorescence with a power efficiency of over 100 lm W−1 Adv. Mater. 2016 28 2638 2643 10.1002/adma.201503782 26833580
96. Sasabe H Ultrahigh power efficiency thermally activated delayed fluorescent OLEDs by the strategic use of electron‐transport materials Adv. Opt. Mater. 2018 6 1800376 10.1002/adom.201800376
97. Zhang X Host-free yellow-green organic light-emitting diodes with external quantum efficiency over 20% based on a compound exhibiting thermally activated delayed fluorescence ACS Appl. Mater. Interfaces 2019 11 12693 12698 10.1021/acsami.8b18798 30835427
98. Liu H Modulating the acceptor structure of dicyanopyridine based TADF emitters: Nearly 30% external quantum efficiency and suppression on efficiency roll-off in OLED Chem. Eng. J. 2020 401 126107 10.1016/j.cej.2020.126107
99. Chen C-H New bipolar host materials for high power efficiency green thermally activated delayed fluorescence OLEDs Chem. Eng. J. 2022 442 136292 10.1016/j.cej.2022.136292
100. Zhang Q Efficient blue organic light-emitting diodes employing thermally activated delayed fluorescence Nat. Photonics 2014 8 326 332 10.1038/nphoton.2014.12
101. Hirata S Highly efficient blue electroluminescence based on thermally activated delayed fluorescence Nat. Mater. 2015 14 330 336 10.1038/nmat4154 25485987
102. Sun JW Thermally activated delayed fluorescence from azasiline based intramolecular charge-transfer emitter (DTPDDA) and a highly efficient blue light emitting diode Chem. Mat. 2015 27 6675 6681 10.1021/acs.chemmater.5b02515
103. Komatsu R Sasabe H Seino Y Nakao K Kido J Light-blue thermally activated delayed fluorescent emitters realizing a high external quantum efficiency of 25% and unprecedented low drive voltages in OLEDs J. Mater. Chem. C 2016 4 2274 2278 10.1039/C5TC04057D
104. Lee I Lee JY Molecular design of deep blue fluorescent emitters with 20% external quantum efficiency and narrow emission spectrum Org. Electron. 2016 29 160 164 10.1016/j.orgel.2015.12.001
105. Lee SY Adachi C Yasuda T High-efficiency blue organic light-emitting diodes based on thermally activated delayed fluorescence from phenoxaphosphine and phenoxathiin derivatives Adv. Mater. 2016 28 4626 4631 10.1002/adma.201506391 27059783
106. Lin TA Sky-blue organic light emitting diode with 37% external quantum efficiency using thermally activated delayed fluorescence from spiroacridine-triazine hybrid Adv. Mater. 2016 28 6976 6983 10.1002/adma.201601675 27271917
107. Rajamalli P A method for reducing the singlet-triplet energy gaps of TADF materials for improving the blue OLED efficiency ACS Appl. Mater. Interfaces 2016 8 27026 27034 10.1021/acsami.6b10678 27648600
108. Sun JW Kim KH Moon CK Lee JH Kim JJ Highly efficient sky-blue fluorescent organic light emitting diode based on mixed cohost system for thermally activated delayed fluorescence emitter (2CzPN) ACS Appl. Mater. Interfaces 2016 8 9806 9810 10.1021/acsami.6b00286 27019330
109. Rajamalli P Thermally activated delayed fluorescence emitters with a m,m-di-tert-butyl-carbazolyl benzoylpyridine core achieving extremely high blue electroluminescence efficiencies J. Mater. Chem. C 2017 5 2919 2926 10.1039/C7TC00457E
110. Xu Y Highly efficient blue fluorescent OLEDs based on upper level triplet-singlet intersystem crossing Adv. Mater. 2019 31 e1807388 10.1002/adma.201807388 30714207
111. Bian J Ambipolar self-host functionalization accelerates blue multi-resonance thermally activated delayed fluorescence with internal quantum efficiency of 100 Adv. Mater. 2022 34 e2110547 10.1002/adma.202110547 35233858
112. Cheon HJ Woo SJ Baek SH Lee JH Kim YH Dense local triplet states and steric shielding of a multi-resonance TADF emitter enable high-performance deep-blue OLEDs Adv. Mater. 2022 34 e2207416 10.1002/adma.202207416 36222388
113. Mei Y Liu D Li J Wang J Accelerating PLQY and RISC rates in deep-blue TADF materials with the acridin-9(10H)-one acceptor by tuning the peripheral groups on carbazole donors J. Mater. Chem. C 2022 10 16524 16535 10.1039/D2TC03448D
114. Matsushima T Adachi C Enhanced hole injection and transport in molybdenum-dioxide-doped organic hole-transporting layers J. Appl. Phys. 2008 103 034501 10.1063/1.2836972
115. Kim K-H Moon C-K Sun JW Sim B Kim J-J Triplet harvesting by a conventional fluorescent emitter using reverse intersystem crossing of host triplet exciplex Adv. Opt. Mater. 2015 3 895 899 10.1002/adom.201400644
116. Zhao B Highly efficient red OLEDs using DCJTB as the dopant and delayed fluorescent exciplex as the host Sci. Rep. 2015 5 10697 10.1038/srep10697 26023882
117. Hung WY Balance the carrier mobility to achieve high performance exciplex OLED using a triazine-based acceptor ACS Appl. Mater. Interfaces 2016 8 4811 4818 10.1021/acsami.5b11895 26820247
118. Lo YC High-efficiency red and near-infrared organic light-emitting diodes enabled by pure organic fluorescent emitters and an exciplex-forming cohost ACS Appl. Mater. Interfaces 2019 11 23417 23427 10.1021/acsami.9b06612 31252481
119. Xia G Organoboron compounds constructed through the tautomerization of 1H-indole to 3H-indole for red OLEDs J. Mater. Chem. C 2021 9 6834 6840 10.1039/D1TC01537K
120. Bang, H.-S., Yun, J. & Lee, C. Improved lifetime and efficiency of green organic light-emitting diodes with a fluorescent dye (C545T)-doped hole transport layer. In Proc. SPIE, Organic Light Emitting Materials and Devices XI (eds. Kafafi, Z. H. & So, F.) 66551W-1–66551W-7 (SPIE, 2007).
121. Benor A Takizawa S-y Pérez-Bolívar C Anzenbacher P Efficiency improvement of fluorescent OLEDs by tuning the working function of PEDOT:PSS using UV–ozone exposure Org. Electron. 2010 11 938 945 10.1016/j.orgel.2010.02.014
122. Liu XK Nearly 100% triplet harvesting in conventional fluorescent dopant-based organic light-emitting devices through energy transfer from exciplex Adv. Mater. 2015 27 2025 2030 10.1002/adma.201500013 25676085
123. Jang HJ Lee JY Suppressed nonradiative decay of an exciplex by an inert host for efficiency improvement in a green fluorescence organic light-emitting diode J. Phys. Chem. C 2019 123 26856 26861 10.1021/acs.jpcc.9b08261
124. Liang B Wang J Cheng Z Wei J Wang Y Exciplex-based electroluminescence: over 21% external quantum efficiency and approaching 100 lm/W power efficiency J. Phys. Chem. Lett. 2019 10 2811 2816 10.1021/acs.jpclett.9b01140 31082247
125. Zheng C-J Highly efficient non-doped deep-blue organic light-emitting diodes based on anthracene derivatives J. Mater. Chem. 2010 20 1560 1566 10.1039/b918739a
126. Sych G Exciplex-enhanced singlet emission efficiency of nondoped organic light emitting diodes based on derivatives of tetrafluorophenylcarbazole and tri/tetraphenylethylene exhibiting aggregation-induced emission enhancement J. Phys. Chem. C 2018 122 14827 14837 10.1021/acs.jpcc.8b03895
127. Tasaki S Realization of ultra‐high‐efficient fluorescent blue OLED J. Soc. Inf. Disp. 2022 30 441 451 10.1002/jsid.1127
128. Zhao J Highly efficient green and red OLEDs based on a new exciplex system with simple structures Org. Electron. 2017 43 136 141 10.1016/j.orgel.2017.01.020
129. Shih CJ Versatile exciplex-forming co-host for improving efficiency and lifetime of fluorescent and phosphorescent organic light-emitting diodes ACS Appl. Mater. Interfaces 2018 10 24090 24098 10.1021/acsami.8b08281 29943574
130. Reineke S Walzer K Leo K Triplet-exciton quenching in organic phosphorescent light-emitting diodes with Ir-based emitters Phys. Rev. B 2007 75 125328 10.1103/PhysRevB.75.125328
131. Fukagawa H Highly efficient and stable red phosphorescent organic light-emitting diodes using platinum complexes Adv. Mater. 2012 24 5099 5103 10.1002/adma.201202167 22887861
132. Kwak J New carbazole-based host material for low-voltage and highly efficient red phosphorescent organic light-emitting diodes J. Mater. Chem. 2012 22 6351 6355 10.1039/c2jm15138c
133. Chen C-H Highly efficient orange and deep-red organic light emitting diodes with long operational lifetimes using carbazole–quinoline based bipolar host materials J. Mater. Chem. C 2014 2 6183 6191 10.1039/C4TC00523F
134. Lee JH Shin H Kim JM Kim KH Kim JJ Exciplex-forming co-host-based red phosphorescent organic light-emitting diodes with long operational stability and high efficiency ACS Appl. Mater. Interfaces 2017 9 3277 3281 10.1021/acsami.6b14438 28098969
135. Jia L High-performance exciplex-type host for multicolor phosphorescent organic light-emitting diodes with low turn-on voltages ACS Sustain. Chem. Eng. 2018 6 8809 8815 10.1021/acssuschemeng.8b01155
136. Liu X-Y 9-Silafluorene and 9-germafluorene: novel platforms for highly efficient red phosphorescent organic light-emitting diodes J. Mater. Chem. C 2018 6 8144 8151 10.1039/C8TC02851F
137. Wang Y High-efficiency red organic light-emitting diodes based on a double-emissive layer with an external quantum efficiency over 30% J. Mater. Chem. C 2018 6 7042 7045 10.1039/C8TC01639A
138. Ito T A series of dibenzofuran-based n-type exciplex host partners realizing high-efficiency and stable deep-red phosphorescent OLEDs Chem. Eur. J. 2019 25 7308 7314 10.1002/chem.201805907 30741443
139. Tian QS Multichannel effect of triplet excitons for highly efficient green and red phosphorescent OLEDs Adv. Opt. Mater. 2020 8 2000556 10.1002/adom.202000556
140. Kim S-Y Organic light-emitting diodes with 30% external quantum efficiency based on a horizontally oriented emitter Adv. Funct. Mater. 2013 23 3896 3900 10.1002/adfm.201300104
141. Li G Very high efficiency orange-red light-emitting devices with low roll-off at high luminance based on an ideal host-guest system consisting of two novel phosphorescent iridium complexes with bipolar transport Adv. Funct. Mater. 2014 24 7420 7426 10.1002/adfm.201402177
142. Liu J Achieving above 30% external quantum efficiency for inverted phosphorescence organic light-emitting diodes based on ultrathin emitting layer Org. Electron. 2014 15 2492 2498 10.1016/j.orgel.2014.07.027
143. Seo S Exciplex-triplet energy transfer: a new method to achieve extremely efficient organic light-emitting diode with external quantum efficiency over 30% and drive voltage below 3 V Japn J. Appl. Phys. 2014 53 042102 10.7567/JJAP.53.042102
144. Shih CJ Exciplex-forming cohost for high efficiency and high stability phosphorescent organic light-emitting diodes ACS Appl. Mater. Interfaces 2018 10 2151 2157 10.1021/acsami.7b15034 29265796
145. Tsai MH 3-(9-Carbazolyl)carbazoles and 3,6-di(9-carbazolyl)carbazoles as effective host materials for efficient blue organic electrophosphorescence Adv. Mater. 2007 19 862 866 10.1002/adma.200600822
146. Su S-J Takahashi Y Chiba T Takeda T Kido J Structure-property relationship of pyridine-containing triphenyl benzene electron-transport materials for highly efficient blue phosphorescent OLEDs Adv. Funct. Mater. 2009 19 1260 1267 10.1002/adfm.200800809
147. Lee J Lee J-I Lee J-W Chu HY Effects of charge balance on device performances in deep blue phosphorescent organic light-emitting diodes Org. Electron. 2010 11 1159 1164 10.1016/j.orgel.2010.04.014
148. Jeon SO Jang SE Son HS Lee JY External quantum efficiency above 20% in deep blue phosphorescent organic light-emitting diodes Adv. Mater. 2011 23 1436 1441 10.1002/adma.201004372 21433109
149. Lee CW Lee JY Above 30% external quantum efficiency in blue phosphorescent organic light-emitting diodes using pyrido[2,3-b]indole derivatives as host materials Adv. Mater. 2013 25 5450 5454 10.1002/adma.201301091 23788128
150. Fleetham T Li G Wen L Li J Efficient ‘pure’ blue OLEDs employing tetradentate Pt complexes with a narrow spectral bandwidth Adv. Mater. 2014 26 7116 7121 10.1002/adma.201401759 25207726
151. Udagawa K Sasabe H Cai C Kido J Low-driving-voltage blue phosphorescent organic light-emitting devices with external quantum efficiency of 30% Adv. Mater. 2014 26 5062 5066 10.1002/adma.201401621 24975629
152. Lee J-H An exciplex forming host for highly efficient blue organic light emitting diodes with low driving voltage Adv. Funct. Mater. 2015 25 361 366 10.1002/adfm.201402707
153. Lim H An exciplex host for deep-blue phosphorescent organic light-emitting diodes ACS Appl. Mater. Interfaces 2017 9 37883 37887 10.1021/acsami.7b10914 28968060
154. Wang Z Manipulation of thermally activated delayed fluorescence of blue exciplex emission: fully utilizing exciton energy for highly efficient organic light emitting diodes with low roll-off ACS Appl. Mater. Interfaces 2017 9 21346 21354 10.1021/acsami.7b04987 28581709
155. Idris M Blue emissive fac/mer‐iridium (III) NHC carbene complexes and their application in OLEDs Adv. Opt. Mater. 2021 9 2001994 10.1002/adom.202001994
156. Inoue M Effect of reverse intersystem crossing rate to suppress efficiency roll-off in organic light-emitting diodes with thermally activated delayed fluorescence emitters Chem. Phys. Lett. 2016 644 62 67 10.1016/j.cplett.2015.11.042
157. Yang M Park IS Yasuda T Full-color, narrowband, and high-efficiency electroluminescence from boron and carbazole embedded polycyclic heteroaromatics J. Am. Chem. Soc. 2020 142 19468 19472 10.1021/jacs.0c10081 33151672
158. Oda S Carbazole-based DABNA analogues as highly efficient thermally activated delayed fluorescence materials for narrowband organic light-emitting diodes Angew. Chem. Int. Ed. 2021 60 2882 2886 10.1002/anie.202012891
159. Huang T Wang Q Meng G Duan L Zhang D Accelerating radiative decay in blue through-space charge transfer emitters by minimizing the face-to-face donor-acceptor distances Angew. Chem. Int. Ed. 2022 61 e202200059 10.1002/anie.202200059
160. Lv X Extending the pi-skeleton of multi-resonance TADF materials towards high-efficiency narrowband deep-blue emission Angew. Chem. Int. Ed. 2022 61 e202201588 10.1002/anie.202201588
161. Grüne J Bunzmann N Meinecke M Dyakonov V Sperlich A Kinetic modeling of transient electroluminescence reveals TTA as an efficiency-limiting process in exciplex-based TADF OLEDs J. Phys. Chem. C 2020 124 25667 25674 10.1021/acs.jpcc.0c06528
162. Virtanen P SciPy 1.0: fundamental algorithms for scientific computing in Python Nat. Methods 2020 17 261 272 10.1038/s41592-019-0686-2 32015543
